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1 decimal integer ring cycle of many

Quantum Field Fractal Polarization Math Constants

nemeth braille printable arx calc

pronounced why phi prime quotients

ᐱ Y φ Θ P Q Ψ

condensed matter

Y Phi Theta Prime Q Psi Quotient Based Numerals 

nu mer numer nu mer i call numerical nomenclature & arc ratio constants

Q represents a ratio quotient of a prime number divided by a prime number

Q=(⅄p/⅄p) so ∈1⅄Q=(Pn2/Pn1) and ∈2⅄Q=(Pn1/Pn2)

Prime consecutive step tier base rationals of 2:199 of the 10 digit prime 1,000,000,007

1st tier 46 primes example 10 tiers to 9 divisions of primes with primes (p) or (P) P→Q→∈2⅄Q ∈1⅄Q

∈3⅄Q does not exist where numbers of p have no decimals path variant of cn

2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 

2nd tier 1st divide steps in decimal value with cycle decimal key in bold with ^ repeat notation at start of decimal cycle for calculation variable change when factoring decimals of multiple cycle strain stem(s) factored ratios of later prime divided by previous prime of prime consecutive order.  

Path of Q base ∈1⅄Q 

examples of ∈1⅄1Qn1=(pn2/pn1) 

∈1⅄1Qn1 prime consecutive later divided by previous cycles back in remainder back to the first division remainder.

have not read this anywhere . . . this may help with the mersenne prime search of primes.

if 1⅄P=(pn2/pn1)=1⅄1Qn1 consecutive prime later divided by previous cycles back in remainder back to the first remainder then the prime no matter the number of digits when later prime divided by the next previous of consecutive primes will cycle back to the first remainder. The first 45 variables of 1⅄P=(pn2/pn1)=1⅄1Qn1 prove that fact. Both 2⅄P=(pn1/pn2)=2⅄1Qn equation combined with 1⅄P=(pn2/pn1)=1⅄1Qn1 equation can varify as functions of P with Q bases if primes are consecutive no matter the number of digits to the prime numbers.

1⅄1Qn1=(pn2/pn1)=(3/2)=1.5

1⅄1Qn2=(pn3/pn2)=(5/3)=1.^6

1⅄1Qn3=(pn4/pn3)=(7/5)=1.4

1⅄1Qn4=(pn5/pn4)=(11/7)=1.^571428

1⅄1Qn5=(pn6/pn5)=(13/11)=1.^18

1⅄1Qn6=(pn7/pn6)=(17/13)=1.^307692

1⅄1Qn7=(pn8/pn7)=(19/17)=1.^1176470588235294

1⅄1Qn8=(pn9/pn8)=(23/19)=1.^210526315789473684

1⅄1Qn9=(pn10/pn9)=(29/23)=1.^2608695652173913043478

1⅄1Qn10=(pn11/pn10)=(31/29)=1.^0689655172413793103448275862

1⅄1Qn11=(pn/pn)=(37/31)=1.^193548387096774

1⅄1Qn12=(pn/pn)=(41/37)=1.^108

1⅄1Qn13=(pn/pn)=(43/41)=1.^04878

1⅄1Qn14=(pn/pn)=(47/43)=1.^093023255813953488372

1⅄1Qn15=(pn/pn)=(53/47)=1.^12765957446808510638297872340425531914893610702

1⅄1Qn16=(pn/pn)=(59/53)=1.^1132075471698

1⅄1Qn17=(pn/pn)=(61/59)=1.^0338983050847457627118644067796610169491525423728813559322

1⅄1Qn18=(pn/pn)=(67/61)=1.^098360655737704918032786885245901639344262295081967213114754

1⅄1Qn19=(pn/pn)=(71/67)=1.^059701492537313432835820895522388

1⅄1Qn20=(pn/pn)=(73/71)=1.^02816901408450704225352112676056338

1⅄1Qn21=(pn/pn)=(79/73)=1.^08219178

1⅄1Qn22=(pn/pn)=(83/79)=1.^0506329113924

1⅄1Qn23=(pn/pn)=(89/83)=1.^07228915662650602409638554216867469879518

1⅄1Qn24=(pn/pn)=(97/89)=1.^08988764044943820224719101123595505617977528

1⅄1Qn25=(pn/pn)=(101/97)=1.^04123092783505154639175257731958762886597938144329896907216494845360820618

1⅄1Qn26=(pn/pn)=(103/101)=1.^0198

1⅄1Qn27=(pn/pn)=(107/103)=1.^0388349514563106796111662136504854368932

1⅄1Qn28=(pn/pn)=(109/107)=1.^01869158878504672897196261682242990654205607476635514

1⅄1Qn29=(pn/pn)=(113/109)=1.^0366972477064220183486238532110091743119266055045871559633027522935779816513758712844

1⅄1Qn30=(pn/pn)=(127/113)=1.^123893805308849557522

1⅄1Qn31=(pn/pn)=(131/127)=1.^031496062992125984251968503937007874015748

1⅄1Qn32=(pn/pn)=(137/131)=1.^045801526717557251908396946564885496183206106870229007633587786259541984732824427480916030534351145038167938931297099236641221374

1⅄1Qn33=(pn/pn)=(139/137)=1.^01459854

1⅄1Qn34=(pn/pn)=(149/139)=1.^071942446043165474820143884892086330935251798561151080291955395683453237410

1⅄1Qn35=(pn/pn)=(151/149)=1.^01343624295302

1⅄1Qn36=(pn/pn)=(157/151)=1.^0397350993377483443708609271523178807284768211920529801324503311258278145695364238410596026490066225165562913907218543046357615894

1⅄1Qn37=(pn/pn)=(163/157)=1.^038216560509554140127388535031847133757961783439490445859872611464968152866242

1⅄1Qn38=(pn/pn)=(167/163)=1.^024539877300613496932515337423312883435582822085889570552147239263803680981595092

1⅄1Qn39=(pn/pn)=(173/167)=1.^0359281437125748502994011976047904191616766467065868263473053892215568862275449101796407185628742514970059880239520958083832335329341317365269461077844311377245508982

1⅄1Qn40=(pn/pn)=(179/173)=1.^034682080924554913294797687861271676300578

1⅄1Qn41=(pn/pn)=(181/179)=1.^0111731843575418994413407821229050279329608936536312849162

1⅄1Qn42=(pn/pn)=(191/181)=1.^005524861878453038674033149171270718232044198895027624309392265193370165745856353591160220994475138121546961325966850828729281767955801104972375690607734806629834254143646408839779

1⅄1Qn43=(pn/pn)=(193/191)=1.^01047120418848167539267015706806282722513089005235602094240837696335078534031413612565445026178

1⅄1Qn44=(pn/pn)=(197/193)=1.^02072538860103626943005181347150259067357512953367875647668393782383419689119170984455958549222797927461139896373069948186528497409326424870466321243523316062176165803108808290155440414507772

1⅄1Qn45=(pn/pn)=(199/197)=1.^01015228426395939086294416243654822335025380710659898477157360406091370558375634517766497461928934

Prime consecutive step tier base rationals of 2:199 of the 10 digit prime 1,000,000,007

1st tier 46 primes example 10 tiers to 9 divisions of primes with primes (p) or (P) P→Q→∈2⅄Q ∈1⅄Q

∈3⅄Q does not exist where numbers of p have no decimals path variant of cn

2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 

2nd tier 1st divide steps in decimal value with cycle decimal key in bold with ^ repeat notation at start of decimal cycle for calculation variable change when factoring decimals of multiple cycle strain stem(s) factored ratios of previous prime divided by consecutive later prime.  

Alternate path P→Q→∈2⅄1Qn1=(pn1/pn2) 

∈2⅄1 prime consecutive previous divided by later cycles back in remainder back to the dividend. 

have not read this anywhere . . . this may help with the mersenne prime search of primes.

if 2⅄P=(pn1/pn2)=2⅄1Qn1 consecutive prime previous divided by later cycles back in remainder back to the dividend then the prime no matter the number of digits when previous prime divided by the next later consecutive prime will cycle back to the dividend. The first 45 variables of 2⅄P=(pn1/pn2)=2⅄1Qn prove that fact.

2⅄1Qn1=(pn1/pn2)=(2/3)=0.^6 

2⅄1Qn2=(pn2/pn3)=(3/5)=0.6 

2⅄1Qn3=(pn3/pn4)=(5/7)=0.^714285 

2⅄1Qn4=(pn4/pn5)=(7/11)=0.^63 

2⅄1Qn5=(pn5/pn6)=(11/13)=0.^846153 

2⅄1Qn6=(pn6/pn7)=(13/17)=0.^7647058823529411 

2⅄1Qn7=(pn7/pn8)=(17/19)=0.^894736842105263157 

2⅄1Qn8=(pn8/pn9)=(19/23)=0.^8260869565217391304347

2⅄1Qn9=(pn9/pn10)=(23/29)=0.^7931034482758620689655172413

2⅄1Qn10=(pn10/pn11)=(29/31)=0.^935483870967741

2⅄1Qn11=(pn11/pn12)=(31/37)=0.^837

2⅄1Qn12=(pn12/pn13)=(37/41)=0.^9024390243

2⅄1Qn13=(pn13/pn14)=(41/43)=0.^953488372093023255813

2⅄1Qn14=(pn14/pn15)=(43/47)=0.^9148936170212765957446808510638297872340425531

2⅄1Qn15=(pn15/pn16)=(47/53)=0.^88679245283018867924528301

2⅄1Qn16=(pn16/pn17)=(53/59)=0.^8983050847457627118644067796610169491525423728813559322033

2⅄1Qn17=(pn17/pn18)=(59/61)=0.^967213114754098360655737704918032786885245901639344262295081

2⅄1Qn18=(pn18/pn19)=(61/67)=0.^910447761194029850746268656716417

2⅄1Qn19=(pn19/pn20)=(67/71)=0.^94366197183098591549295774647887323

2⅄1Qn20=(pn20/pn21)=(71/73)=0.^97260273

2⅄1Qn21=(pn21/pn22)=(73/79)=0.^9240506329113

2⅄1Qn22=(pn22/pn23)=(79/83)=0.^95180722891566265060240963855421686746987

2⅄1Qn23=(pn23/pn24)=(83/89)=0.^93258426966292134831460674157303370786516853

2⅄1Qn24=(pn24/pn25)=(89/97)=0.^917525773195876288659793814432989690721649484536082474226804123711340206185567010309278350515463

2⅄1Qn25=(pn25/pn26)=(97/101)=0.^9603

2⅄1Qn26=(pn26/pn27)=(101/103)=0.^9805825242718446601941747572815533

2⅄1Qn27=(pn27/pn28)=(103/107)=0.^96261682242990654205607476635514018691588785046728971

2⅄1Qn28=(pn28/pn29)=(107/109)=0.^0981651376146788990825688073394495412844036697247706422018348623853211009174311926605504587155963302752293577

2⅄1Qn29=(pn29/pn30)=(109/113)=0.^9646017699115044247787610619469026548672566371681415929203539823008849557522123893805309734513274336283185840707

2⅄1Qn30=(pn30/pn31)=(113/127)=0.^88976377952755905511811023622047244094481

2⅄1Qn31=(pn31/pn32)=(127/131)=0.^969465648854961832061068015267175572519083

2⅄1Qn32=(pn32/pn33)=(131/137)=0.^95620437

2⅄1Qn33=(pn33/pn34)=(137/139)=0.^9856115107913669064748201438848920863309352517

2⅄1Qn34=(pn34/pn35)=(139/149)=0.^932885906040268456375838926174496651006711409395973154362416107382550335570469798657718120805369127516778523489

2⅄1Qn35=(pn35/pn36)=(149/151)=0.^986754966887417218543046357615894039735099337748344370860927152317880794701

2⅄1Qn36=(pn36/pn37)=(151/157)=0.^961783439490445859872611464968152866242038216560509554140127388535031847133757

2⅄1Qn37=(pn37/pn38)=(157/163)=0.^963190184049079754601226993865030674846625766871165644171779141104294478527607361

2⅄1Qn38=(pn38/pn39)=(163/167)=0.^9760479041916167664670658682634730538922155688622754491017964071856287425149700598802395209580838323353293413173652694610778443113772455089820359281437125748502994011

2⅄1Qn39=(pn39/pn40)=(167/173)=0.^9653179190751445086705202312138728323699421

2⅄1Qn40=(pn40/pn41)=(173/179)=0.^96648044692737430167597765363128491620111731843575418994413407821229050279329608938547486033519553072625698324022346336871508379888268156424581005586592178770949720670391061452513

2⅄1Qn41=(pn41/pn42)=(179/181)=0.^9889502762430939226519337016574585635359116022099447513812154696132596685082877292817679558011049723756906077348066298342541436464088397790055248618784530386740331491712707182320441

2⅄1Qn42=(pn42/pn43)=(181/191)=0.^94764397905759162303664921465968586387434554973821989528795811518324607329842931937172774869109

2⅄1Qn43=(pn43/pn44)=(191/193)=0.^989637304699481864284974093264248704663212435233160621761658031088082901554404145077720207253886010362694300518134715025906735751295336787564766839378238341917098445595854922279792746113

2⅄1Qn44=(pn44/pn45)=(193/197)=0.^979695431

2⅄1Qn45=(pn45/pn46)=(197/199)=0.^989949748743718592964824120603015075025125628140703517587939698492462311557763819095477386934673366834170854271356783919597


3rd tier 2nd Prime 1⅄(2⅄1Q) base

Variants ∈ next set of prime radical decimal stem path factoring to the degree of the variant decimal cycles per array.

Quadratic equations dependent of 4 prime radicals decimal cycle limit or break in stem numeral factoring.

Factoring  for variables of ∈2Qnc1  and so on →. . .

∈(Qn2/Qn1c1)=(0.6/0.6)=1

∈2Qn1=1

Variant prime radical divide

∈(Qn2/Qn1c2)=0.6/0.66=0.9^09

(Qn2/Qn1c3)=0.6/0.666=0.9^009 and so on →. . .

then

∈(Qn3c1/Qn2)=0.714285/0.6=1.190475

∈2Qn2=1.190475

(Qn3c2/Qn2)=0.714285714285/0.6=1.1904759523808^3 and so on →. . .

then

∈(Qn4c1/Qn3c1)=0.63/0.714285=0.8^819994 and so on →. . .

∈2Qn3=0.8^819994 

∈(Qn5c1/Qn4c1)=0.^846153/0.^63=1.3431

∈2Qn4=1.3431

∈(Qn6c1/Qn5c1)=0.^7647058823529411/0.^846153=0.9037442192^522405

∈2Qn5=0.9037442192^522405

and so on →. . .

1⅄2Q divide starting at 1⅄(Qn2/Qn1) then 2⅄2Q divide starting at 2⅄(Qn1/Qn2)

WHILE

in short 1(Qn2/Qn1) is not 2(Qn1/Qn2)

1⅄(1⅄2Q)n1=(1⅄1Q)n2/(1⅄1Q)n1 is not 2⅄(1⅄2Q)n2=(1⅄1Q)n1/(1⅄1Q)n2

4th tier 3rd Prime 1⅄(1⅄(2⅄1Q) base

Variants ∈ next set of prime radical decimal stem path factoring to the degree of the variant decimal cycles per array.

Quadratic equations dependent of 4 prime radicals decimal cycle limit or break in stem numeral factoring.

Factoring  for variables of ∈3Qnc1  and so on →. . .

∈{(Qn4/Qn3)/(Qn2/Qn1)}=2Qn2/2Qn1=^0.9/1=0.9

∈3Qn1=0.9 

then {(Qn4/Qn3)c2/(Qn2/Qn1)}=2Qn2c2/2Qn1=^0.909/1=0.909 and so on →. . . where c2 is applicable to {(Qn4/Qn3)c2

∈{(Qn5/Qn4)/(Qn3/Qn2)}=2Qn3/2Qn2=1.190475/^0.9=1.32275

∈3Qn2=1.32275

then {(Qn5/Qn4)/(Qn3/Qn2)c2}=2Qn3/2Qn2c2=1.190475/^0.909=1.210^6435 and so on →. . .

∈{(Qn6/Qn5)/(Qn4/Qn3)}=2Qn4/2Qn3=0.8^819994/1.190475=0.740^880236

∈3Qn3=0.740^880236

then {(Qn6/Qn5)c2/(Qn4/Qn3)}=2Qn4c2/2Qn3=0.8^819994819994/1.190475=0.740880305^759801 and so on →. . .

5th tier 4th Prime 1⅄(1⅄(1⅄(2⅄1Q) base

Variants ∈ next set of prime radical decimal stem path factoring to the degree of the variant decimal cycles per array.

Quadratic equations dependent of 4 prime radicals decimal cycle limit or break in stem numeral factoring.

Factoring  for variables of ∈4Qnc1  and so on →. . .

∈(3Qn2/3Qn1)=1.4679

4Qn1=1.4679

then ∈(3Qn2/3Qn1c2)=1.45^517

∈(3Qn3/3Qn2)=0.5601060^18522

4Qn2=0.5601060^18522

then ∈(3Qn3c2/3Qn2)=0.560106019187^477603 and so on . . .

6th tier 5th Prime 1⅄(1⅄(1⅄(1⅄(2⅄1Q) base

Variants ∈ next set of prime radical decimal stem path factoring to the degree of the variant decimal cycles per array.

Quadratic equations dependent of 4 prime radicals decimal cycle limit or break in stem numeral factoring.

Factoring  for variables of ∈5Qnc1  and so on →. . .

∈(3Qn3/3Qn2)/(3Qn2/3Qn1)=(4Qn2/4Qn1)=(0.5601060^18522/1.4679)

∈5Qn1=0.3815696018270999386879215205395462906192519926425505824647455548744464881803937597929014238027113563594182199059881470113767967845221064105184277685809660058587097213706655766741603651474896110089243136453436882621472852374139465222426595817153757067920158489134137202806730703726411880918318686559029906669391647932420464609303767286599906256556986170720076299475441106342393896041964779617140132165913890592002799850126030383541113154847039989100076299475441106342393896041964711492608488316642823080591320934668574153552694325226514067715784453981878874582737243681449690033371020505^48402479732951835956809046937802302609160956195926153007698072071667007745827372436814496900333810205054

⅄Q Alternate Base Path Variants 2nd tier of Q and third divide of P prime base quotient ratios

1⅄(1⅄Qn2/1⅄Qn1) and 1⅄(2⅄Qn2/2⅄Qn1) are the first ratio definitions of the sets structured from each equation.

∈1⅄2Q for each is then respectably 1⅄2Q of (1⅄Qn2/1⅄Qn1) and 1⅄2Q of (2⅄Qn2/2⅄Qn1)

Then if 

L=∈1⅄(1⅄Qn2/2⅄Qn1)

K=∈2⅄(1⅄Qn1/2⅄Qn2)

U=∈1⅄(2⅄Qn2/1⅄Qn1)

J=∈2⅄(2⅄Qn1/1⅄Qn2)

Path Set ∈1⅄2Q pertains to base equations

1⅄2Q of (1⅄Qn2/1⅄Qn1) and 1⅄2Q of (2⅄Qn2/2⅄Qn1) and (L) 1⅄2Q of (1⅄Qn2/2⅄Qn1) and (U) 1⅄2Q of (2⅄Qn2/1⅄Qn1)


Then

1⅄(1⅄2Q)n1=[1⅄2Q=(1⅄Qn2c1/1⅄Qn1c1)]=(1.^6/1.5)=1.0^6

1⅄(1⅄2Q)n2=[1⅄2Q=(1⅄Qn3c1/1⅄Qn2c1)]=(1.4/1.^6)=0.875

1⅄(1⅄2Q)n3=[1⅄2Q=(1⅄Qn4c1/1⅄Qn3c1)]=(1.^571428/1.4)=1.12244^857142

1⅄(1⅄2Q)n4=[1⅄2Q=(1⅄Qn5c1/1⅄Qn4c1)]=(1.^18/1.^571428)

1⅄(1⅄2Q)n5=[1⅄2Q=(1⅄Qn6c1/1⅄Qn5c1)]=(1.^307692/1.^18)

1⅄(1⅄2Q)n6=[1⅄2Q=(1⅄Qn7c1/1⅄Qn6c1)]=(1.^1176470588235294/1.^307692)

1⅄(1⅄2Q)n7=[1⅄2Q=(1⅄Qn8c1/1⅄Qn7c1)]=(1.^210526315789473684/1.^1176470588235294)

1⅄(1⅄2Q)n8=[1⅄2Q=(1⅄Qn9c1/1⅄Qn8c1)]=(1.^2608695652173913043478/1.^210526315789473684)

1⅄(1⅄2Q)n9=[1⅄2Q=(1⅄Qn10c1/1⅄Qn9c1)]=(1.^0689655172413793103448275862/1.^2608695652173913043478)

1⅄(1⅄2Q)n10=[1⅄2Q=(1⅄Qn11c1/1⅄Qn10c1)]=(1.^193548387096774/1.^0689655172413793103448275862)

1⅄(1⅄2Q)n11=[1⅄2Q=(1⅄Qn12c1/1⅄Qn11c1)]=(1.^108/1.^193548387096774)

1⅄(1⅄2Q)n12=[1⅄2Q=(1⅄Qn13c1/1⅄Qn12c1)]=(1.^04878/1.^108)

1⅄(1⅄2Q)n13=[1⅄2Q=(1⅄Qn14c1/1⅄Qn13c1)]=(1.^093023255813953488372/1.^04878)

1⅄(1⅄2Q)n14=[1⅄2Q=(1⅄Qn15c1/1⅄Qn14c1)]=(1.^12765957446808510638297872340425531914893610702/1.^093023255813953488372)

1⅄(1⅄2Q)n15=[1⅄2Q=(1⅄Qn16c1/1⅄Qn15c1)]=(1.^1132075471698/1.^12765957446808510638297872340425531914893610702)

1⅄(1⅄2Q)n16=[1⅄2Q=(1⅄Qn17c1/1⅄Qn16c1)]=(1.^0338983050847457627118644067796610169491525423728813559322/1.^1132075471698)

1⅄(1⅄2Q)n17=[1⅄2Q=(1⅄Qn18c1/1⅄Qn17c1)]=(1.^098360655737704918032786885245901639344262295081967213114754/1.^0338983050847457627118644067796610169491525423728813559322)

1⅄(1⅄2Q)n18=[1⅄2Q=(1⅄Qn19c1/1⅄Qn18c1)]=(1.^059701492537313432835820895522388/1.^098360655737704918032786885245901639344262295081967213114754)

1⅄(1⅄2Q)n19=[1⅄2Q=(1⅄Qn20c1/1⅄Qn19c1)]=(1.^02816901408450704225352112676056338/1.^059701492537313432835820895522388)

1⅄(1⅄2Q)n20=[1⅄2Q=(1⅄Qn21c1/1⅄Qn20c1)]=(1.^08219178/1.^02816901408450704225352112676056338)

1⅄(1⅄2Q)n21=[1⅄2Q=(1⅄Qn22c1/1⅄Qn21c1)]=(1.^0506329113924/1.^08219178)

1⅄(1⅄2Q)n22=[1⅄2Q=(1⅄Qn23c1/1⅄Qn22c1)]=(1.^07228915662650602409638554216867469879518/1.^0506329113924)

1⅄(1⅄2Q)n23=[1⅄2Q=(1⅄Qn24c1/1⅄Qn23c1)]=(1.^08988764044943820224719101123595505617977528/1.^07228915662650602409638554216867469879518)

1⅄(1⅄2Q)n24=[1⅄2Q=(1⅄Qn25c1/1⅄Qn24c1)]=(1.^04123092783505154639175257731958762886597938144329896907216494845360820618/1.^08988764044943820224719101123595505617977528)

1⅄(1⅄2Q)n25=[1⅄2Q=(1⅄Qn26c1/1⅄Qn25c1)]=(1.^0198/1.^04123092783505154639175257731958762886597938144329896907216494845360820618)

1⅄(1⅄2Q)n26=[1⅄2Q=(1⅄Qn27c1/1⅄Qn26c1)]=(1.^0388349514563106796111662136504854368932/1.^0198)

1⅄(1⅄2Q)n27=[1⅄2Q=(1⅄Qn28c1/1⅄Qn27c1)]=(1.^01869158878504672897196261682242990654205607476635514/1.^0388349514563106796111662136504854368932)

1⅄(1⅄2Q)n28=[1⅄2Q=(1⅄Qn29c1/1⅄Qn28c1)]=(1.^0366972477064220183486238532110091743119266055045871559633027522935779816513758712844/1.^01869158878504672897196261682242990654205607476635514)

1⅄(1⅄2Q)n29=[1⅄2Q=(1⅄Qn30c1/1⅄Qn29c1)]=(1.^123893805308849557522/1.^0366972477064220183486238532110091743119266055045871559633027522935779816513758712844)

1⅄(1⅄2Q)n30=[1⅄2Q=(1⅄Qn31c1/1⅄Qn30c1)]=(1.^031496062992125984251968503937007874015748/1.^123893805308849557522)

1⅄(1⅄2Q)n31=[1⅄2Q=(1⅄Qn32c1/1⅄Qn31c1)]=(1.^045801526717557251908396946564885496183206106870229007633587786259541984732824427480916030534351145038167938931297099236641221374/1.^031496062992125984251968503937007874015748)

1⅄(1⅄2Q)n32=[1⅄2Q=(1⅄Qn33c1/1⅄Qn32c1)]=(1.^01459854/1.^045801526717557251908396946564885496183206106870229007633587786259541984732824427480916030534351145038167938931297099236641221374)

1⅄(1⅄2Q)n33=[1⅄2Q=(1⅄Qn34c1/1⅄Qn33c1)]=(1.^071942446043165474820143884892086330935251798561151080291955395683453237410/1.^01459854)

1⅄(1⅄2Q)n34=[1⅄2Q=(1⅄Qn35c1/1⅄Qn34c1)]=(1.^01343624295302/1.^071942446043165474820143884892086330935251798561151080291955395683453237410)

1⅄(1⅄2Q)n35=[1⅄2Q=(1⅄Qn36c1/1⅄Qn35c1)]=(1.^0397350993377483443708609271523178807284768211920529801324503311258278145695364238410596026490066225165562913907218543046357615894/1.^01343624295302)

1⅄(1⅄2Q)n36=[1⅄2Q=(1⅄Qn37c1/1⅄Qn36c1)]=(1.^038216560509554140127388535031847133757961783439490445859872611464968152866242/1.^0397350993377483443708609271523178807284768211920529801324503311258278145695364238410596026490066225165562913907218543046357615894)

1⅄(1⅄2Q)n37=[1⅄2Q=(1⅄Qn38c1/1⅄Qn37c1)]=(1.^024539877300613496932515337423312883435582822085889570552147239263803680981595092/1.^038216560509554140127388535031847133757961783439490445859872611464968152866242)

1⅄(1⅄2Q)n38=[1⅄2Q=(1⅄Qn39c1/1⅄Qn38c1)]=(1.^0359281437125748502994011976047904191616766467065868263473053892215568862275449101796407185628742514970059880239520958083832335329341317365269461077844311377245508982/1.^024539877300613496932515337423312883435582822085889570552147239263803680981595092)

1⅄(1⅄2Q)n39=[1⅄2Q=(1⅄Qn40c1/1⅄Qn39c1)]=(1.^034682080924554913294797687861271676300578/1.^0359281437125748502994011976047904191616766467065868263473053892215568862275449101796407185628742514970059880239520958083832335329341317365269461077844311377245508982)

1⅄(1⅄2Q)n40=[1⅄2Q=(1⅄Qn41c1/1⅄Qn40c1)]=(1.^0111731843575418994413407821229050279329608936536312849162/1.^034682080924554913294797687861271676300578)

1⅄(1⅄2Q)n41=[1⅄2Q=(1⅄Qn42c1/1⅄Qn41c1)]=(1.^005524861878453038674033149171270718232044198895027624309392265193370165745856353591160220994475138121546961325966850828729281767955801104972375690607734806629834254143646408839779/1.^0111731843575418994413407821229050279329608936536312849162)

1⅄(1⅄2Q)n42=[1⅄2Q=(1⅄Qn43c1/1⅄Qn42c1)]=(1.^01047120418848167539267015706806282722513089005235602094240837696335078534031413612565445026178/1.^005524861878453038674033149171270718232044198895027624309392265193370165745856353591160220994475138121546961325966850828729281767955801104972375690607734806629834254143646408839779)

1⅄(1⅄2Q)n43=[1⅄2Q=(1⅄Qn44c1/1⅄Qn43c1)]=(1.^02072538860103626943005181347150259067357512953367875647668393782383419689119170984455958549222797927461139896373069948186528497409326424870466321243523316062176165803108808290155440414507772/1.^01047120418848167539267015706806282722513089005235602094240837696335078534031413612565445026178)

1⅄(1⅄2Q)n44=[1⅄2Q=(1⅄Qn45c1/1⅄Qn44c1)]=(1.^01015228426395939086294416243654822335025380710659898477157360406091370558375634517766497461928934/1.^02072538860103626943005181347150259067357512953367875647668393782383419689119170984455958549222797927461139896373069948186528497409326424870466321243523316062176165803108808290155440414507772)

and so on for variables of ∈1⅄(1⅄2Q)n=[1⅄2Q=(1⅄Qn2cn/1⅄Qn1cn)] that vary to degrees of stem cycle count variant 1⅄(1⅄2Q)ncn


Functions applicable to variables of ∈1⅄(1⅄2Q)ncn=[1⅄2Q=(1⅄Qn2cn/1⅄Qn1cn)]


X⅄=(n2xn1) example X⅄(1⅄2Q)n=[X2Q=(1⅄Qn2cnx1⅄Qn1cn)] 


+⅄=(nncn+nncn) example +⅄(1⅄2Q)n=[+⅄2Q=(1⅄Qn2cn+1⅄Qn1cn)]


1-⅄=(n2-n1) example 1-⅄(1⅄2Q)n=[1-⅄2Q=(1⅄Qn2cn-1⅄Qn1cn)]

3rd tier of Q and 4th divide of P prime base quotient ratios

Then example 1⅄(1⅄3Q)n1 of (1⅄2Qn2c1/1⅄2Qn1c1)] so

1⅄(1⅄3Q)n1 of (1⅄2Qn2c1/1⅄2Qn1c1)]=(0.875/1.0^6)=0.82^5471698113207

1⅄(1⅄3Q)n2 of (1⅄2Qn3c1/1⅄2Qn2c1)]=(1.12244^857142/0.875)=1.28279836733^714285

1⅄(1⅄3Q)n of (1⅄2Qn4c1/1⅄2Qn3c1)]=[(1⅄Qn5c1/1⅄Qn4c1)/(1⅄Qn4c1/1⅄Qn3c1)]=[(1.^18/1.^571428)/(1.^571428/1.4)]

and so on for variables of ∈1⅄(1⅄3Q)ncn of (1⅄2Qn2c1/1⅄2Qn1c1)] 


4th tier of Q and 5th divide of P prime base quotient ratios

Then example 1⅄(1⅄4Q)n1 of (1⅄3Qn2c1/1⅄3Qn1c1)] so

1⅄(1⅄4Q)n1 of (1⅄3Qn2c1/1⅄3Qn1c1)]=(1.28279836733^714285/0.82^5471698113207)

1⅄(1⅄4Q)n1 of (1⅄3Qn2c1/1⅄3Qn1c1)]=[(1⅄2Qn4c1/1⅄2Qn3c1)/(1⅄2Qn3c1/1⅄2Qn2c1)]

and so on for variables of ∈1⅄(1⅄4Q)ncn of (1⅄3Qn2c1/1⅄3Qn1c1)] 


Again ⅄Q Alternate Base Path Variants 2nd tier of Q and third divide of P prime base quotient ratios

if ∈1⅄2Q=[1⅄(1⅄2Q)=(1⅄Qn2cn/1⅄Qn1cn)] and ∈1⅄2Q=[1⅄(2⅄2Q)=(2⅄Qn2cn/2⅄Qn1cn)] if ∈1⅄2Q=(Nn2cn/Nn1cn)

Then ∈1⅄2Q=[1⅄(2⅄2Q)=(2⅄Qn2cn/2⅄Qn1cn)]=[(Pn2/Pn3)/(Pn1/Pn2)]=[(3/5)/(2/3)]=(0.6/0.^6)=1 if cn of 2⅄Qn1cn ia 1 stem decimal cycle for variable 2⅄Qn1c1

1⅄(1⅄2Q)n1=[1⅄2Q=(2⅄Qn2c1/2⅄Qn1c1)]=(0.6/0.^6)=1

1⅄(1⅄2Q)n2=[1⅄2Q=(2⅄Qn3c1/2⅄Qn2c1)]=(0.^714285/0.6)=1.190475

1⅄(1⅄2Q)n3=[1⅄2Q=(2⅄Qn4c1/2⅄Qn3c1)]=(0.^63/0.^714285)=0.^882000

1⅄(1⅄2Q)n4=[1⅄2Q=(2⅄Qn5c1/2⅄Qn4c1)]=(0.^846153/0.^63)=1.3431

1⅄(1⅄2Q)n5=[1⅄2Q=(2⅄Qn6c1/2⅄Qn5c1)]=(0.^7647058823529411/0.^846153)=0.9037442192^522405

1⅄(1⅄2Q)n6=[1⅄2Q=(2⅄Qn7c1/2⅄Qn6c1)]=(0.^894736842105263157/0.^7647058823529411)=1.17^0040485829959630

1⅄(1⅄2Q)n7=[1⅄2Q=(2⅄Qn8c1/2⅄Qn7c1)]=(0.^8260869565217391304347/0.^894736842105263157)=0.9232^736572890025584679383631713554996444089514066496172914677749360613819973501278772378525855854219948849114091148337595907937620560102301790290561

1⅄(1⅄2Q)n8=[1⅄2Q=(2⅄Qn9c1/2⅄Qn8c1)]=(0.^7931034482758620689655172413/0.^8260869565217391304347)=0.960072^595281306715063616878306896551724137940635199110707803992741431940963702359346642564246727949183303085309056251742286751361162484572542649727767695195825675317604355716888003620163339382940109852993595281306715063616878306896551724137940635199110707803992741431940963702359346642564246727949183303085309056251742286751361162484572542649727767695195825675317604355716888003620163339382940109852993

1⅄(1⅄2Q)n9=[1⅄2Q=(2⅄Qn10c1/2⅄Qn9c1)]=(0.^935483870967741/0.^7931034482758620689655172413)

1⅄(1⅄2Q)n10=[1⅄2Q=(2⅄Qn11c1/2⅄Qn10c1)]=(0.^837/0.^935483870967741)

1⅄(1⅄2Q)n11=[1⅄2Q=(2⅄Qn12c1/2⅄Qn11c1)]=(0.^9024390243/0.^837)

1⅄(1⅄2Q)n12=[1⅄2Q=(2⅄Qn13c1/2⅄Qn12c1)]=(0.^953488372093023255813/0.^9024390243)

1⅄(1⅄2Q)n13=[1⅄2Q=(2⅄Qn14c1/2⅄Qn13c1)]=(0.^9148936170212765957446808510638297872340425531/0.^953488372093023255813)

1⅄(1⅄2Q)n14=[1⅄2Q=(2⅄Qn15c1/2⅄Qn14c1)]=(0.^88679245283018867924528301/0.^9148936170212765957446808510638297872340425531)

1⅄(1⅄2Q)n15=[1⅄2Q=(2⅄Qn16c1/2⅄Qn15c1)]=(0.^8983050847457627118644067796610169491525423728813559322033/0.^88679245283018867924528301)

1⅄(1⅄2Q)n16=[1⅄2Q=(2⅄Qn17c1/2⅄Qn16c1)]=(0.^967213114754098360655737704918032786885245901639344262295081/0.^8983050847457627118644067796610169491525423728813559322033)

1⅄(1⅄2Q)n17=[1⅄2Q=(2⅄Qn18c1/2⅄Qn17c1)]=(0.^910447761194029850746268656716417/0.^967213114754098360655737704918032786885245901639344262295081)

1⅄(1⅄2Q)n18=[1⅄2Q=(2⅄Qn19c1/2⅄Qn18c1)]=(0.^94366197183098591549295774647887323/0.^910447761194029850746268656716417)

1⅄(1⅄2Q)n19=[1⅄2Q=(2⅄Qn20c1/2⅄Qn19c1)]=(0.^97260273/0.^94366197183098591549295774647887323)

1⅄(1⅄2Q)n20=[1⅄2Q=(2⅄Qn21c1/2⅄Qn20c1)]=(0.^9240506329113/0.^97260273)

1⅄(1⅄2Q)n21=[1⅄2Q=(2⅄Qn22c1/2⅄Qn21c1)]=(0.^95180722891566265060240963855421686746987/0.^9240506329113)

1⅄(1⅄2Q)n22=[1⅄2Q=(2⅄Qn23c1/2⅄Qn22c1)]=(0.^93258426966292134831460674157303370786516853/0.^95180722891566265060240963855421686746987)

1⅄(1⅄2Q)n23=[1⅄2Q=(2⅄Qn24c1/2⅄Qn23c1)]=(0.^917525773195876288659793814432989690721649484536082474226804123711340206185567010309278350515463/0.^93258426966292134831460674157303370786516853)

1⅄(1⅄2Q)n24=[1⅄2Q=(2⅄Qn25c1/2⅄Qn24c1)]=(0.^9603/0.^917525773195876288659793814432989690721649484536082474226804123711340206185567010309278350515463)

1⅄(1⅄2Q)n25=[1⅄2Q=(2⅄Qn26c1/2⅄Qn25c1)]=(0.^9805825242718446601941747572815533/0.^9603)

1⅄(1⅄2Q)n26=[1⅄2Q=(2⅄Qn27c1/2⅄Qn26c1)]=(0.^96261682242990654205607476635514018691588785046728971/0.^9805825242718446601941747572815533)

1⅄(1⅄2Q)n27=[1⅄2Q=(2⅄Qn28c1/2⅄Qn27c1)]=(0.^0981651376146788990825688073394495412844036697247706422018348623853211009174311926605504587155963302752293577/0.^96261682242990654205607476635514018691588785046728971)

1⅄(1⅄2Q)n28=[1⅄2Q=(2⅄Qn29c1/2⅄Qn28c1)]=(0.^9646017699115044247787610619469026548672566371681415929203539823008849557522123893805309734513274336283185840707/0.^0981651376146788990825688073394495412844036697247706422018348623853211009174311926605504587155963302752293577)

1⅄(1⅄2Q)n29=[1⅄2Q=(2⅄Qn30c1/2⅄Qn29c1)]=(0.^88976377952755905511811023622047244094481/0.^9646017699115044247787610619469026548672566371681415929203539823008849557522123893805309734513274336283185840707)

1⅄(1⅄2Q)n30=[1⅄2Q=(2⅄Qn31c1/2⅄Qn30c1)]=(0.^969465648854961832061068015267175572519083/0.^88976377952755905511811023622047244094481)

1⅄(1⅄2Q)n31=[1⅄2Q=(2⅄Qn32c1/2⅄Qn31c1)]=(0.^95620437/0.^969465648854961832061068015267175572519083)

1⅄(1⅄2Q)n32=[1⅄2Q=(2⅄Qn33c1/2⅄Qn32c1)]=(0.^9856115107913669064748201438848920863309352517/0.^95620437)

1⅄(1⅄2Q)n33=[1⅄2Q=(2⅄Qn34c1/2⅄Qn33c1)]=(0.^932885906040268456375838926174496651006711409395973154362416107382550335570469798657718120805369127516778523489/0.^9856115107913669064748201438848920863309352517)

1⅄(1⅄2Q)n34=[1⅄2Q=(1⅄Qn35c1/2⅄Qn34c1)]=(0.^986754966887417218543046357615894039735099337748344370860927152317880794701/0.^932885906040268456375838926174496651006711409395973154362416107382550335570469798657718120805369127516778523489)

1⅄(1⅄2Q)n35=[1⅄2Q=(2⅄Qn36c1/2⅄Qn35c1)]=(0.^961783439490445859872611464968152866242038216560509554140127388535031847133757/0.^986754966887417218543046357615894039735099337748344370860927152317880794701)

1⅄(1⅄2Q)n36=[1⅄2Q=(2⅄Qn37c1/2⅄Qn36c1)]=(0.^963190184049079754601226993865030674846625766871165644171779141104294478527607361/0.^961783439490445859872611464968152866242038216560509554140127388535031847133757)

1⅄(1⅄2Q)n37=[1⅄2Q=(2⅄Qn38c1/2⅄Qn37c1)]=(0.^9760479041916167664670658682634730538922155688622754491017964071856287425149700598802395209580838323353293413173652694610778443113772455089820359281437125748502994011/0.^963190184049079754601226993865030674846625766871165644171779141104294478527607361)

1⅄(1⅄2Q)n38=[1⅄2Q=(2⅄Qn39c1/2⅄Qn38c1)]=(0.^9653179190751445086705202312138728323699421/0.^9760479041916167664670658682634730538922155688622754491017964071856287425149700598802395209580838323353293413173652694610778443113772455089820359281437125748502994011)

1⅄(1⅄2Q)n39=[1⅄2Q=(2⅄Qn40c1/2⅄Qn39c1)]=(0.^96648044692737430167597765363128491620111731843575418994413407821229050279329608938547486033519553072625698324022346336871508379888268156424581005586592178770949720670391061452513/0.^9653179190751445086705202312138728323699421)

1⅄(1⅄2Q)n40=[1⅄2Q=(2⅄Qn41c1/2⅄Qn40c1)]=(0.^9889502762430939226519337016574585635359116022099447513812154696132596685082877292817679558011049723756906077348066298342541436464088397790055248618784530386740331491712707182320441/0.^96648044692737430167597765363128491620111731843575418994413407821229050279329608938547486033519553072625698324022346336871508379888268156424581005586592178770949720670391061452513)

1⅄(1⅄2Q)n41=[1⅄2Q=(2⅄Qn42c1/2⅄Qn41c1)]=(0.^94764397905759162303664921465968586387434554973821989528795811518324607329842931937172774869109/0.^9889502762430939226519337016574585635359116022099447513812154696132596685082877292817679558011049723756906077348066298342541436464088397790055248618784530386740331491712707182320441)

1⅄(1⅄2Q)n42=[1⅄2Q=(2⅄Qn43c1/2⅄Qn42c1)]=(0.^989637304699481864284974093264248704663212435233160621761658031088082901554404145077720207253886010362694300518134715025906735751295336787564766839378238341917098445595854922279792746113/0.^94764397905759162303664921465968586387434554973821989528795811518324607329842931937172774869109)

1⅄(1⅄2Q)n43=[1⅄2Q=(2⅄Qn44c1/2⅄Qn43c1)]=(0.^979695431/0.^989637304699481864284974093264248704663212435233160621761658031088082901554404145077720207253886010362694300518134715025906735751295336787564766839378238341917098445595854922279792746113)

1⅄(1⅄2Q)n44=[1⅄2Q=(2⅄Qn45c1/2⅄Qn44c1)]=(0.^989949748743718592964824120603015075025125628140703517587939698492462311557763819095477386934673366834170854271356783919597/0.^979695431)

and so on for variables of ∈1⅄(2⅄2Q)n=[1⅄2Q=(2⅄Qn2cn/2⅄Qn1cn)] that vary to degrees of stem cycle count variant 1⅄(2⅄2Q)ncn


Functions applicable to variables of ∈1⅄(1⅄2Q)ncn=[1⅄2Q=(2⅄Qn2cn/2⅄Qn1cn)]


X⅄=(n2xn1) example X⅄(1⅄2Q)n=[X2Q=(2⅄Qn2cnx2⅄Qn1cn)] 


+⅄=(nncn+nncn) example +⅄(1⅄2Q)n=[+⅄2Q=(2⅄Qn2cn+2⅄Qn1cn)]


1-⅄=(n2-n1) example 1-⅄(1⅄2Q)n=[2-⅄2Q=(1⅄Qn2cn-2⅄Qn1cn)]


3rd tier of Q and 4th divide of P prime base quotient ratios

Then example 1⅄(1⅄3Q)n1 of (2⅄2Qn2c1/2⅄2Qn1c1)] so

1⅄(1⅄3Q)n1 of (2⅄2Qn2c1/2⅄2Qn1c1)]=(1.190475/1)=1.190475

1⅄(1⅄3Q)n2 of (2⅄2Qn3c1/2⅄2Qn2c1)]=(0.^882000/1.190475)=^0.74088 or 0.74088^074088

1⅄(1⅄3Q)n3 of (2⅄2Qn4c1/2⅄2Qn4c1)]=(1.3431/0.^882000)

1⅄(1⅄3Q)n4 of (2⅄2Qn5c1/2⅄2Qn4c1)]=(0.9037442192^522405/1.3431)

1⅄(1⅄3Q)n5 of (2⅄2Qn6c1/2⅄2Qn5c1)]=(1.17^0040485829959630/0.9037442192^522405)

1⅄(1⅄3Q)n6 of (2⅄2Qn7c1/2⅄2Qn6c1)]=(0.9232^736572890025584679383631713554996444089514066496172914677749360613819973501278772378525855854219948849114091148337595907937620560102301790290561/1.17^0040485829959630)

1⅄(1⅄3Q)n7 of (2⅄2Qn8c1/2⅄2Qn7c1)]=(0.960072^595281306715063616878306896551724137940635199110707803992741431940963702359346642564246727949183303085309056251742286751361162484572542649727767695195825675317604355716888003620163339382940109852993595281306715063616878306896551724137940635199110707803992741431940963702359346642564246727949183303085309056251742286751361162484572542649727767695195825675317604355716888003620163339382940109852993/0.9232^736572890025584679383631713554996444089514066496172914677749360613819973501278772378525855854219948849114091148337595907937620560102301790290561)


1⅄(1⅄3Q)n8 of (2⅄2Qn9c1/2⅄2Qn8c1)]=[(2⅄Qn10c1/2⅄Qn9c1)/(2⅄Qn9c1/2⅄Qn8c1)]


1⅄(1⅄3Q)n9 of (2⅄2Qn10c1/2⅄2Qn9c1)]=[(2⅄Qn11c1/2⅄Qn10c1)/(2⅄Qn10c1/2⅄Qn9c1)]


and so on for variables of ∈1⅄(1⅄3Q)ncn of (2⅄2Qn2c1/2⅄2Qn1c1)] from 2⅄Q variables of Prime P base consecutives


4th tier of Q and 5th divide of P prime base quotient ratios

Then example 1⅄(1⅄4Q)n1 of [(1⅄(1⅄3Q)n2~(2⅄2Qn3c1/2⅄2Qn2c1)]/2⅄2Qn1c1) / 1⅄(1⅄3Q)n1~(2⅄2Qn2c1/2⅄2Qn1c1)]] so

1⅄(1⅄4Q)n1 of [(1⅄(1⅄3Q)n2/1⅄(1⅄3Q)n1=[(0.^882000/1.190475)/(1.190475/1)]=(0.74088/1.190475)=0.6^223398

1⅄(1⅄4Q)n2 of [(1⅄(1⅄3Q)n3/1⅄(1⅄3Q)n2=[(2⅄2Qn4c1/2⅄2Qn4c1)/(2⅄2Qn3c1/2⅄2Qn2c1)]

and so on for variables of ∈1⅄(1⅄4Q)n1 of [(1⅄(1⅄3Q)n2/1⅄(1⅄3Q)n1 from variables of ∈1⅄(1⅄3Q)ncn of (2⅄2Qn2c1/2⅄2Qn1c1)] derived from  2⅄Q variables of Prime P base consecutives


⅄Q Alternate Base Path Variants 2nd tier of Q and third divide of P prime base quotient ratios

1⅄(1⅄Qn2/1⅄Qn1) and 1⅄(2⅄Qn2/2⅄Qn1) are the first ratio definitions of the sets structured from each equation.

∈1⅄2Q for each is then respectably 1⅄2Q of (1⅄Qn2/1⅄Qn1) and 1⅄2Q of (2⅄Qn2/2⅄Qn1)

Then if 

L=∈1⅄(1⅄Qn2/2⅄Qn1)

K=∈2⅄(1⅄Qn1/2⅄Qn2)

U=∈1⅄(2⅄Qn2/1⅄Qn1)

J=∈2⅄(2⅄Qn1/1⅄Qn2)

Path Set ∈1⅄2Q pertains to base equations

1⅄2Q of (1⅄Qn2/1⅄Qn1) and 1⅄2Q of (2⅄Qn2/2⅄Qn1) and (L) 1⅄2Q of (1⅄Qn2/2⅄Qn1) and (U) 1⅄2Q of (2⅄Qn2/1⅄Qn1)

So then 

2⅄(1⅄Qn1/1⅄Qn2) and 2⅄(2⅄Qn1/2⅄Qn2) for ∈2⅄2Q each is then respectably 2⅄2Q of (1⅄Qn1/1⅄Qn2) and 2⅄2Q of (2⅄Qn1/2⅄Qn2) that differ from sets ∈L ∈K ∈U and ∈J

2⅄2Qn1 of (1⅄Qn1/1⅄Qn2)=(1.5/1.^6)

2⅄2Qn2 of (1⅄Qn2/1⅄Qn3)=(1.^6/1.4)

2⅄2Qn3 of (1⅄Qn3/1⅄Qn4)=(1.4/1.^571428)

2⅄2Qn4 of (1⅄Qn4/1⅄Qn5)=(1.^571428/1.^18)

2⅄2Qn5 of (1⅄Qn5/1⅄Qn6)=(1.^18/1.^307692)

2⅄2Qn6 of (1⅄Qn6/1⅄Qn7)=(1.^307692/1.^1176470588235294)

2⅄2Qn7 of (1⅄Qn7/1⅄Qn8)=(1.^1176470588235294/1.^210526315789473684)

2⅄2Qn8 of (1⅄Qn8/1⅄Qn9)=(1.^210526315789473684/1.^2608695652173913043478)

2⅄2Qn9 of (1⅄Qn9/1⅄Qn10)=(1.^2608695652173913043478/1.^0689655172413793103448275862)

2⅄2Qn10 of (1⅄Qn10/1⅄Qn11)=(1.^0689655172413793103448275862/1.^193548387096774)

2⅄2Qn11 of (1⅄Qn11/1⅄Qn12)=(1.^193548387096774/1.^108)

2⅄2Qn12 of (1⅄Qn12/1⅄Qn13)=(1.^108/1.^04878)

2⅄2Qn13 of (1⅄Qn13/1⅄Qn14)=(1.^04878/1.^093023255813953488372)

2⅄2Qn14 of (1⅄Qn14/1⅄Qn15)=(1.^093023255813953488372/1.^12765957446808510638297872340425531914893610702)

2⅄2Qn15 of (1⅄Qn15/1⅄Qn16)=(1.^12765957446808510638297872340425531914893610702/1.^1132075471698)

2⅄2Qn16 of (1⅄Qn16/1⅄Qn17)=(1.^1132075471698/1.^0338983050847457627118644067796610169491525423728813559322)

2⅄2Qn17 of (1⅄Qn17/1⅄Qn18)=(1.^0338983050847457627118644067796610169491525423728813559322/1.^098360655737704918032786885245901639344262295081967213114754)

2⅄2Qn18 of (1⅄Qn18/1⅄Qn19)=(1.^098360655737704918032786885245901639344262295081967213114754/1.^059701492537313432835820895522388)

2⅄2Qn19 of (1⅄Qn19/1⅄Qn20)=(1.^059701492537313432835820895522388/1.^02816901408450704225352112676056338)

2⅄2Qn20 of (1⅄Qn20/1⅄Qn21)=(1.^02816901408450704225352112676056338/1.^08219178)

2⅄2Qn21 of (1⅄Qn21/1⅄Qn22)=(1.^08219178/1.^0506329113924)

2⅄2Qn22 of (1⅄Qn22/1⅄Qn23)=(1.^0506329113924/1.^07228915662650602409638554216867469879518)

2⅄2Qn23 of (1⅄Qn23/1⅄Qn24)=(1.^07228915662650602409638554216867469879518/1.^08988764044943820224719101123595505617977528)

2⅄2Qn24 of (1⅄Qn24/1⅄Qn25)=(1.^08988764044943820224719101123595505617977528/1.^04123092783505154639175257731958762886597938144329896907216494845360820618)

2⅄2Qn25 of (1⅄Qn25/1⅄Qn26)=(1.^04123092783505154639175257731958762886597938144329896907216494845360820618/1.^0198)

2⅄2Qn26 of (1⅄Qn26/1⅄Qn27)=(1.^0198/1.^0388349514563106796111662136504854368932)

2⅄2Qn27 of (1⅄Qn27/1⅄Qn28)=(1.^0388349514563106796111662136504854368932/1.^01869158878504672897196261682242990654205607476635514)

2⅄2Qn28 of (1⅄Qn28/1⅄Qn29)=(1.^01869158878504672897196261682242990654205607476635514/1.^0366972477064220183486238532110091743119266055045871559633027522935779816513758712844)

2⅄2Qn29 of (1⅄Qn29/1⅄Qn30)=(1.^0366972477064220183486238532110091743119266055045871559633027522935779816513758712844/1.^123893805308849557522)

2⅄2Qn30 of (1⅄Qn30/1⅄Qn31)=(1.^123893805308849557522/1.^031496062992125984251968503937007874015748)

2⅄2Qn31 of (1⅄Qn31/1⅄Qn32)=(1.^031496062992125984251968503937007874015748/1.^045801526717557251908396946564885496183206106870229007633587786259541984732824427480916030534351145038167938931297099236641221374)

2⅄2Qn32 of (1⅄Qn32/1⅄Qn33)=(1.^045801526717557251908396946564885496183206106870229007633587786259541984732824427480916030534351145038167938931297099236641221374/1.^01459854)

2⅄2Qn33 of (1⅄Qn33/1⅄Qn34)=(1.^01459854/1.^071942446043165474820143884892086330935251798561151080291955395683453237410)

2⅄2Qn34 of (1⅄Qn34/1⅄Qn35)=(1.^071942446043165474820143884892086330935251798561151080291955395683453237410/1.^01343624295302)

2⅄2Qn35 of (1⅄Qn35/1⅄Qn36)=(1.^01343624295302/1.^0397350993377483443708609271523178807284768211920529801324503311258278145695364238410596026490066225165562913907218543046357615894)

2⅄2Qn36 of (1⅄Qn36/1⅄Qn37)=(1.^0397350993377483443708609271523178807284768211920529801324503311258278145695364238410596026490066225165562913907218543046357615894/1.^038216560509554140127388535031847133757961783439490445859872611464968152866242)

2⅄2Qn37 of (1⅄Qn37/1⅄Qn38)=(1.^038216560509554140127388535031847133757961783439490445859872611464968152866242/1.^024539877300613496932515337423312883435582822085889570552147239263803680981595092)

2⅄2Qn38 of (1⅄Qn38/1⅄Qn39)=(1.^024539877300613496932515337423312883435582822085889570552147239263803680981595092/1.^0359281437125748502994011976047904191616766467065868263473053892215568862275449101796407185628742514970059880239520958083832335329341317365269461077844311377245508982)

2⅄2Qn39 of (1⅄Qn39/1⅄Qn40)=(1.^0359281437125748502994011976047904191616766467065868263473053892215568862275449101796407185628742514970059880239520958083832335329341317365269461077844311377245508982/1.^034682080924554913294797687861271676300578)

2⅄2Qn40 of (1⅄Qn40/1⅄Qn41)=(1.^034682080924554913294797687861271676300578/1.^0111731843575418994413407821229050279329608936536312849162)

2⅄2Qn41 of (1⅄Qn41/1⅄Qn42)=(1.^0111731843575418994413407821229050279329608936536312849162/1.^005524861878453038674033149171270718232044198895027624309392265193370165745856353591160220994475138121546961325966850828729281767955801104972375690607734806629834254143646408839779)

2⅄2Qn42 of (1⅄Qn42/1⅄Qn43)=(1.^005524861878453038674033149171270718232044198895027624309392265193370165745856353591160220994475138121546961325966850828729281767955801104972375690607734806629834254143646408839779/1.^01047120418848167539267015706806282722513089005235602094240837696335078534031413612565445026178)

2⅄2Qn43 of (1⅄Qn43/1⅄Qn44)=(1.^01047120418848167539267015706806282722513089005235602094240837696335078534031413612565445026178/1.^02072538860103626943005181347150259067357512953367875647668393782383419689119170984455958549222797927461139896373069948186528497409326424870466321243523316062176165803108808290155440414507772)

2⅄2Qn44 of (1⅄Qn44/1⅄Qn45)=(1.^02072538860103626943005181347150259067357512953367875647668393782383419689119170984455958549222797927461139896373069948186528497409326424870466321243523316062176165803108808290155440414507772/1.^01015228426395939086294416243654822335025380710659898477157360406091370558375634517766497461928934)

Again ⅄Q Alternate Base Path Variants 2nd tier of Q and third divide of P prime base quotient ratios

1⅄(1⅄Qn2/1⅄Qn1) and 1⅄(2⅄Qn2/2⅄Qn1) are the first ratio definitions of the sets structured from each equation.

∈1⅄2Q for each is then respectably 1⅄2Q of (1⅄Qn2/1⅄Qn1) and 1⅄2Q of (2⅄Qn2/2⅄Qn1)

Then if 

L=∈1⅄(1⅄Qn2/2⅄Qn1)

K=∈2⅄(1⅄Qn1/2⅄Qn2)

U=∈1⅄(2⅄Qn2/1⅄Qn1)

J=∈2⅄(2⅄Qn1/1⅄Qn2)

Path Set ∈1⅄2Q pertains to base equations

1⅄2Q of (1⅄Qn2/1⅄Qn1) and 1⅄2Q of (2⅄Qn2/2⅄Qn1) and (L) 1⅄2Q of (1⅄Qn2/2⅄Qn1) and (U) 1⅄2Q of (2⅄Qn2/1⅄Qn1)

So then 

2⅄(1⅄Qn1/1⅄Qn2) and 2⅄(2⅄Qn1/2⅄Qn2) for ∈2⅄2Q each is then respectably 2⅄2Q of (1⅄Qn1/1⅄Qn2) and 2⅄2Q of (2⅄Qn1/2⅄Qn2) that differ from sets ∈L ∈K ∈U and ∈J

2⅄2Qn1 of (2⅄Qn1/2⅄Qn2)=(0.^6/0.6)

2⅄2Qn2 of (2⅄Qn2/2⅄Qn3)=(0.6/0.^714285)

2⅄2Qn3 of (2⅄Qn3/2⅄Qn4)=(0.^714285/0.^63)

2⅄2Qn4 of (2⅄Qn4/2⅄Qn5)=(0.^63/0.^846153)

2⅄2Qn5 of (2⅄Qn5/2⅄Qn6)=(0.^846153/0.^7647058823529411)

2⅄2Qn6 of (2⅄Qn6/2⅄Qn7)=(0.^7647058823529411/0.^894736842105263157)

2⅄2Qn7 of (2⅄Qn7/2⅄Qn8)=(0.^894736842105263157/0.^8260869565217391304347)

2⅄2Qn8 of (2⅄Qn8/2⅄Qn9)=(0.^8260869565217391304347/0.^7931034482758620689655172413)

2⅄2Qn9 of (2⅄Qn9/2⅄Qn10)=(0.^7931034482758620689655172413/0.^935483870967741)

2⅄2Qn10 of (2⅄Qn10/2⅄Qn11)=(0.^935483870967741/0.^837)

2⅄2Qn11 of (2⅄Qn11/2⅄Qn12)=(0.^837/0.^9024390243)

2⅄2Qn12 of (2⅄Qn12/2⅄Qn13)=(0.^9024390243/0.^953488372093023255813)

2⅄2Qn13 of (2⅄Qn13/2⅄Qn14)=(0.^953488372093023255813/0.^9148936170212765957446808510638297872340425531)

2⅄2Qn14 of (2⅄Qn14/2⅄Qn15)=(0.^9148936170212765957446808510638297872340425531/0.^88679245283018867924528301)

2⅄2Qn15 of (2⅄Qn15/2⅄Qn16)=(0.^88679245283018867924528301/0.^8983050847457627118644067796610169491525423728813559322033)

2⅄2Qn16 of (2⅄Qn16/2⅄Qn17)=(0.^8983050847457627118644067796610169491525423728813559322033/0.^967213114754098360655737704918032786885245901639344262295081)

2⅄2Qn17 of (2⅄Qn17/2⅄Qn18)=(0.^967213114754098360655737704918032786885245901639344262295081/0.^910447761194029850746268656716417)

2⅄2Qn18 of (2⅄Qn18/2⅄Qn19)=(0.^910447761194029850746268656716417/0.^94366197183098591549295774647887323)

2⅄2Qn19 of (2⅄Qn19/2⅄Qn20)=(0.^94366197183098591549295774647887323/0.^97260273)

2⅄2Qn20 of (2⅄Qn20/2⅄Qn21)=(0.^97260273/0.^9240506329113)

2⅄2Qn21 of (2⅄Qn21/2⅄Qn22)=(0.^9240506329113/0.^95180722891566265060240963855421686746987)

2⅄2Qn22 of (2⅄Qn22/2⅄Qn23)=(0.^95180722891566265060240963855421686746987/0.^93258426966292134831460674157303370786516853)

2⅄2Qn23 of (2⅄Qn23/2⅄Qn24)=(0.^93258426966292134831460674157303370786516853/0.^917525773195876288659793814432989690721649484536082474226804123711340206185567010309278350515463)

2⅄2Qn24 of (2⅄Qn24/2⅄Qn25)=(0.^917525773195876288659793814432989690721649484536082474226804123711340206185567010309278350515463/0.^9603)

2⅄2Qn25 of (2⅄Qn25/2⅄Qn26)=(0.^9603/0.^9805825242718446601941747572815533)

2⅄2Qn26 of (2⅄Qn26/2⅄Qn27)=(0.^9805825242718446601941747572815533/0.^96261682242990654205607476635514018691588785046728971)

2⅄2Qn27 of (2⅄Qn27/2⅄Qn28)=(0.^96261682242990654205607476635514018691588785046728971/0.^0981651376146788990825688073394495412844036697247706422018348623853211009174311926605504587155963302752293577)

2⅄2Qn28 of (2⅄Qn28/2⅄Qn29)=(0.^0981651376146788990825688073394495412844036697247706422018348623853211009174311926605504587155963302752293577/0.^9646017699115044247787610619469026548672566371681415929203539823008849557522123893805309734513274336283185840707)

2⅄2Qn29 of (2⅄Qn29/2⅄Qn30)=(0.^9646017699115044247787610619469026548672566371681415929203539823008849557522123893805309734513274336283185840707/0.^88976377952755905511811023622047244094481)

2⅄2Qn30 of (2⅄Qn30/2⅄Qn31)=(0.^88976377952755905511811023622047244094481/0.^969465648854961832061068015267175572519083)

2⅄2Qn31 of (2⅄Qn31/2⅄Qn32)=(0.^969465648854961832061068015267175572519083/0.^95620437)

2⅄2Qn32 of (2⅄Qn32/2⅄Qn33)=(0.^95620437/0.^9856115107913669064748201438848920863309352517)

2⅄2Qn33 of (2⅄Qn33/2⅄Qn34)=(0.^9856115107913669064748201438848920863309352517/0.^932885906040268456375838926174496651006711409395973154362416107382550335570469798657718120805369127516778523489)

2⅄2Qn34 of (2⅄Qn34/2⅄Qn35)=(0.^932885906040268456375838926174496651006711409395973154362416107382550335570469798657718120805369127516778523489/0.^986754966887417218543046357615894039735099337748344370860927152317880794701)

2⅄2Qn35 of (2⅄Qn35/2⅄Qn36)=(0.^986754966887417218543046357615894039735099337748344370860927152317880794701/0.^961783439490445859872611464968152866242038216560509554140127388535031847133757)

2⅄2Qn36 of (2⅄Qn36/2⅄Qn37)=(0.^961783439490445859872611464968152866242038216560509554140127388535031847133757/0.^963190184049079754601226993865030674846625766871165644171779141104294478527607361)

2⅄2Qn37 of (2⅄Qn37/2⅄Qn38)=(0.^963190184049079754601226993865030674846625766871165644171779141104294478527607361/0.^9760479041916167664670658682634730538922155688622754491017964071856287425149700598802395209580838323353293413173652694610778443113772455089820359281437125748502994011)

2⅄2Qn38 of (2⅄Qn38/2⅄Qn39)=(0.^9760479041916167664670658682634730538922155688622754491017964071856287425149700598802395209580838323353293413173652694610778443113772455089820359281437125748502994011/0.^9653179190751445086705202312138728323699421)

2⅄2Qn39 of (2⅄Qn39/2⅄Qn40)=(0.^9653179190751445086705202312138728323699421/0.^96648044692737430167597765363128491620111731843575418994413407821229050279329608938547486033519553072625698324022346336871508379888268156424581005586592178770949720670391061452513)

2⅄2Qn40 of (2⅄Qn40/2⅄Qn41)=(0.^96648044692737430167597765363128491620111731843575418994413407821229050279329608938547486033519553072625698324022346336871508379888268156424581005586592178770949720670391061452513/0.^9889502762430939226519337016574585635359116022099447513812154696132596685082877292817679558011049723756906077348066298342541436464088397790055248618784530386740331491712707182320441)

2⅄2Qn41 of (2⅄Qn41/2⅄Qn42)=(0.^9889502762430939226519337016574585635359116022099447513812154696132596685082877292817679558011049723756906077348066298342541436464088397790055248618784530386740331491712707182320441/0.^94764397905759162303664921465968586387434554973821989528795811518324607329842931937172774869109)

2⅄2Qn42 of (2⅄Qn42/2⅄Qn43)=(0.^94764397905759162303664921465968586387434554973821989528795811518324607329842931937172774869109/0.^989637304699481864284974093264248704663212435233160621761658031088082901554404145077720207253886010362694300518134715025906735751295336787564766839378238341917098445595854922279792746113)

2⅄2Qn43 of (2⅄Qn43/2⅄Qn44)=(0.^989637304699481864284974093264248704663212435233160621761658031088082901554404145077720207253886010362694300518134715025906735751295336787564766839378238341917098445595854922279792746113/0.^979695431)

2⅄2Qn44 of (2⅄Qn44/2⅄Qn45)=(0.^979695431/0.^989949748743718592964824120603015075025125628140703517587939698492462311557763819095477386934673366834170854271356783919597)

Prime ∈1⅄2Q and ∈2⅄2Q Base Path Variants

∈1⅄1Qn1 and ∈2⅄1Qn1 with definition of 3⅄ and 2⅄ and 1⅄ sets in prime base of p division logic.

As 3⅄ is not applicable to prime p numerals having no decimal cn change until decimal ratio cell stem cycles are a Q factor.

2⅄ and 1⅄ are paths of p prime consecutive numerals that divide later and previous as explained.

Now paths of two different Q bases labelled as 1Qn1 are in fact not simply 1Qn1

1⅄1Qn1 and 2⅄1Qn1 are paths of p prime consecutive numerals 2⅄ and 1⅄

Each of the variant paths of ⅄1Q can then be reapplied to their own three variant paths 3⅄ and 2⅄ and 1⅄ forming new sets that are not the same sets where cn is a variant factor in each set of the next tier stems cycles and cell definitions.

Variables of sets explained below are applicable to functions with prime p fibonacci y and phi φn base numerals through paths 1⅄, 2⅄, 1X, 1+⅄, 1-⅄, 2-⅄, 3⅄nc ⅄n ⅄ncn numerically.

∈1⅄2Q and ∈2⅄2Q and ∈3⅄2Q then require further definition or symbol notation.

∈1⅄2

∈1⅄2Qn1 of ∈1⅄1Qn1 variables is (1⅄1Qn2/1⅄1Qn1)=(1.^6/1.5)=1.^06 for 1⅄1Qn2c1 variable and (1⅄1Qn2c2/1⅄1Qn1)=(1.^66/1.5)=1.1^06 and so on depending of cn variable factor

∈1⅄2Qn1 of ∈2⅄1Qn1 variables is (2⅄1Qn2/2⅄1Qn1)=(0.6/0.^6)=1 for 2⅄1Qn1c1 variable and (2⅄1Qn2/2⅄1Qn1c2)=(0.6/0.^66)=1.1 and so on depending of cn variable factor

then 

∈1⅄2Qn1 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn2/2⅄1Qn1)=(1.^6/0.^6)=2.^6 depending of cn variable factor c1

and

∈1⅄2Qn1 of ∈2⅄1Qn and ∈1⅄1Qn variables is (2⅄1Qn2/1⅄1Qn1)=(0.6/1.5)=0.4

and are crossed variants of two different path sets variables

∈2⅄2

∈2⅄2Qn1 of ∈1⅄1Qn1 variables is (1⅄1Qn1/1⅄1Qn2)

∈2⅄2Qn1 of ∈2⅄1Qn1 variables is (2⅄1Qn1/2⅄1Qn2)

then 

∈2⅄2Qn1 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn1/2⅄1Qn2) depending of cn variable factor

and

∈2⅄2Qn1 of ∈2⅄1Qn and ∈1⅄1Qn variables is (2⅄1Qn1/1⅄1Qn2) depending of cn variable factor

and are crossed variants of two different path sets variables

∈3⅄2

∈3⅄2Qn1 of ∈1⅄1Qn1 variables is (1⅄1Qn1cn/1⅄1Qn1cn)

∈3⅄2Qn1 of ∈2⅄1Qn1 variables is (2⅄1Qn1cn/2⅄1Qn1cn)

then 

∈3⅄2Qn1 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn1cn/2⅄1Qn1cn) depending of cn variable factor

and

∈3⅄2Qn1 of ∈2⅄1Qn and ∈1⅄1Qn variables is (2⅄1Qn1cn/1⅄1Qn2cn) depending of cn variable factor

and are crossed variants of two different path sets variables

Sets are factorable with AND differ from THESE VARIABLES DEFINITIONS

3rd tiers of Q alternate paths from prime base of ∈3⅄1Qcn sets

∈3⅄(1⅄1Qn)cn/(2⅄1Qn)cn are not same set ∉ yet path of 3⅄ defines variables of same tier level and cn differential factors

and 

∈3⅄(2⅄1Qn)cn/(1⅄1Qn)cn are not same set ∉ yet path of 3⅄ defines variables of same tier level and cn differential factors

and 

∈3⅄(1⅄1Qn)cn/(1⅄1Qn)cn

and 

∈3⅄(2⅄1Qn)cn/(2⅄1Qn)cn 

are applicable ratios to phi and y bases and tiers of the paths of φ of many functions as well as prime path variables sets tiers per variant cycle cn.


∈1⅄ and ∈2⅄ and ∈3⅄ of sets in Q's from P to Y and φ factoring at degrees of cn

∈1⅄3Q=(⅄2Q/⅄2Q)=(⅄1Q/⅄1Q)/(⅄1Q/⅄1Q)=(⅄p/⅄p) that ⅄1Q lacks path root definition of 1⅄1Q or 2⅄1Q from base prime path ⅄P

∈2⅄3Q=(⅄2Q/⅄2Q)=(⅄1Q/⅄1Q)/(⅄1Q/⅄1Q)=(⅄p/⅄p) that ⅄1Q lacks path root definition of 1⅄1Q or 2⅄1Q from base prime path ⅄P

∈3⅄3Q=(⅄2Q/⅄2Q)=(⅄1Q/⅄1Q)/(⅄1Q/⅄1Q)=(⅄p/⅄p) that ⅄1Q lacks path root definition of 1⅄1Q or 2⅄1Q from base prime path ⅄P

So variables of sets ∈1⅄3Q, ∈2⅄3Q, ∈3⅄3Q, ∈1⅄2Q, ∈2⅄2Q, ∈3⅄2Q require definitions of variable from set ∈1⅄1Q or ∈2⅄1Q from base prime path ⅄P.

∈3⅄2Qn1 of ∈1⅄1Qn1 variables is (1⅄1Qn1/1⅄1Qn1)=(1.5/1.5)=1

∈3⅄2Qn2 of ∈1⅄1Qn1 variables is (1⅄1Qn2c1/1⅄1Qn2c2)=(1.^6/1.^66) and so on for cn differentials. . . 

∈3⅄2Qn2 of ∈1⅄1Qn1 variables is (1⅄1Qn2c2/1⅄1Qn2c1)=(1.^66/1.^6) and so on for cn differentials. . . 

∈3⅄2Qn3 of ∈1⅄1Qn1 variables is (1⅄1Qn3/1⅄1Qn3)=(1.4/1.4)=1

∈3⅄2Qn4 of ∈1⅄1Qn1 variables is (1⅄1Qn4c1/1⅄1Qn4c2)=(1.^571428/1.^571428571428) and so on for cn differentials. . . 

∈3⅄2Qn4 of ∈1⅄1Qn1 variables is (1⅄1Qn4c2/1⅄1Qn4c1)=(1.^571428571428/1.^571428) and so on for cn differentials. . . 

∈3⅄2Qn5 of ∈1⅄1Qn1 variables is (1⅄1Qn5c1/1⅄1Qn5c2)=(1.^18/1.^1818) and so on for cn differentials. . . 

∈3⅄2Qn5 of ∈1⅄1Qn1 variables is (1⅄1Qn5c2/1⅄1Qn5c1)=(1.^1818/1.^18) and so on for cn differentials. . . 

∈3⅄2Qn6 of ∈1⅄1Qn1 variables is (1⅄1Qn6c1/1⅄1Qn6c2)=(1.^307692/1.^307692307692) and so on for cn differentials. . . 

∈3⅄2Qn6 of ∈1⅄1Qn1 variables is (1⅄1Qn6c2/1⅄1Qn6c1)=(1.^307692307692/1.^307692) and so on for cn differentials. . . 

∈3⅄2Qn7 of ∈1⅄1Qn1 variables is (1⅄1Qn7c1/1⅄1Qn7c2)=(1.^1176470588235294/1.^11764705882352941176470588235294) and so on for cn differentials. . . 

∈3⅄2Qn7 of ∈1⅄1Qn1 variables is (1⅄1Qn7c2/1⅄1Qn7c1)=(1.^11764705882352941176470588235294/1.^1176470588235294) and so on for cn differentials. . . 

∈3⅄2Qn8 of ∈1⅄1Qn1 variables is (1⅄1Qn8c1/1⅄1Qn8c2)=(1.^210526315789473684/1.^210526315789473684210526315789473684) and so on for cn differentials. . . 

∈3⅄2Qn8 of ∈1⅄1Qn1 variables is (1⅄1Qn8c2/1⅄1Qn8c1)=(1.^210526315789473684210526315789473684/1.^210526315789473684) and so on for cn differentials. . . 

Beginning with 

∈3⅄2Qn1 of ∈2⅄1Qn1 variables is (2⅄1Qn1cn/2⅄1Qn1cn)=(0.^6/0.^6)=1

∈3⅄2Qn1 of ∈2⅄1Qn1 variables is (2⅄1Qn1c1/2⅄1Qn1c2)=(0.^6/0.^66)

∈3⅄2Qn1 of ∈2⅄1Qn1 variables is (2⅄1Qn1c2/2⅄1Qn1c1)=(0.^66/0.^6)=1.1 and so on for cn of variable ∈3⅄2Qn1 of ∈2⅄1Qn1cn

∈3⅄2Qn2 of ∈2⅄1Qn1 variables is (2⅄1Qn2cn/2⅄1Qn2cn)=(0.6/0.6)=1 and has no cn variable change potential in decimal.

∈3⅄2Qn3 of ∈2⅄1Qn1 variables is (2⅄1Qn3cn/2⅄1Qn3cn)=(0.^714285/0.^714285)

∈3⅄2Qn3 of ∈2⅄1Qn1 variables is (2⅄1Qn3c1/2⅄1Qn3c2)=(0.^714285/0.^714285714285)

∈3⅄2Qn3 of ∈2⅄1Qn1 variables is (2⅄1Qn3c2/2⅄1Qn3c1)=(0.^714285714285/0.^714285) and so on for cn of variable ∈3⅄2Qn3 of ∈2⅄1Qn1cn

∈3⅄2Qn4 of ∈2⅄1Qn1 variables is (2⅄1Qn4cn/2⅄1Qn4cn)=(0.^63/0.^63)

∈3⅄2Qn4 of ∈2⅄1Qn1 variables is (2⅄1Qn4c1/2⅄1Qn4c2)=(0.^63/0.^6363)

∈3⅄2Qn4 of ∈2⅄1Qn1 variables is (2⅄1Qn4c2/2⅄1Qn4c1)=(0.^6363/0.^63) and so on for cn of variable ∈3⅄2Qn4 of ∈2⅄1Qn1cn

∈3⅄2Qn5 of ∈2⅄1Qn1 variables is (2⅄1Qn5cn/2⅄1Qn5cn)=(0.^846153/0.^846153)

∈3⅄2Qn5 of ∈2⅄1Qn1 variables is (2⅄1Qn5c1/2⅄1Qn5c2)=(0.^846153/0.^846153846153)

∈3⅄2Qn5 of ∈2⅄1Qn1 variables is (2⅄1Qn5c2/2⅄1Qn5c1)=(0.^846153846153/0.^846153) and so on for cn of variable ∈3⅄2Qn5 of ∈2⅄1Qn1cn

∈3⅄2Qn6 of ∈2⅄1Qn1 variables is (2⅄1Qn6cn/2⅄1Qn6cn)=(0.^7647058823529411/0.^7647058823529411)

∈3⅄2Qn6 of ∈2⅄1Qn1 variables is (2⅄1Qn6c1/2⅄1Qn6c2)=(0.^7647058823529411/0.^76470588235294117647058823529411)

∈3⅄2Qn6 of ∈2⅄1Qn1 variables is (2⅄1Qn6c2/2⅄1Qn6c1)=(0.^76470588235294117647058823529411/0.^7647058823529411) and so on for cn of variable ∈3⅄2Qn6 of ∈2⅄1Qn1cn

∈3⅄2Qn7 of ∈2⅄1Qn1 variables is (2⅄1Qn7cn/2⅄1Qn7cn)=(0.^894736842105263157/0.^894736842105263157)

∈3⅄2Qn7 of ∈2⅄1Qn1 variables is (2⅄1Qn7c1/2⅄1Qn7c2)=(0.^894736842105263157/0.^894736842105263157894736842105263157)

∈3⅄2Qn7 of ∈2⅄1Qn1 variables is (2⅄1Qn7c2/2⅄1Qn7c1)=(0.^894736842105263157894736842105263157/0.^894736842105263157) and so on for cn of variable ∈3⅄2Qn7 of ∈2⅄1Qn1cn

∈3⅄2Qn8 of ∈2⅄1Qn1 variables is (2⅄1Qn8cn/2⅄1Qn8cn)=(0.^8260869565217391304347/0.^8260869565217391304347)

∈3⅄2Qn8 of ∈2⅄1Qn1 variables is (2⅄1Qn8c1/2⅄1Qn8c2)=(0.^8260869565217391304347/0.^82608695652173913043478260869565217391304347)

∈3⅄2Qn8 of ∈2⅄1Qn1 variables is (2⅄1Qn8c2/2⅄1Qn8c1)=(0.^82608695652173913043478260869565217391304347/0.^8260869565217391304347) and so on for cn of variable ∈3⅄2Qn8 of ∈2⅄1Qn1cn

Beginning with

∈3⅄2Qn1 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn1cn/2⅄1Qn1cn) depending of cn variable factor

∈3⅄2Qn1 of ∈1⅄1Qn and ∈2⅄1Qn variables is 

(1⅄1Qn1c1/2⅄1Qn1c1)=(1.5/0.^6)

(1⅄1Qn1c1/2⅄1Qn1c2)=(1.5/0.^66)

(1⅄1Qn1c1/2⅄1Qn1c3)=(1.5/0.^666) and so on for cn variable factor

∈3⅄2Qn2 of ∈1⅄1Qn and ∈2⅄1Qn variables is 

(1⅄1Qn2c1/2⅄1Qn2c1)=(1.^6/0.6)

(1⅄1Qn2c2/2⅄1Qn2c1)=(1.^66/0.6)

(1⅄1Qn2c3/2⅄1Qn2c1)=(1.^666/0.6) and so on for cn variable factor

∈3⅄2Qn3 of ∈1⅄1Qn and ∈2⅄1Qn variables is 

(1⅄1Qn3c1/2⅄1Qn3c1)=(1.4/0.^714285)

(1⅄1Qn3c1/2⅄1Qn3c2)=(1.4/0.^714285714285)

(1⅄1Qn3c1/2⅄1Qn3c3)=(1.4/0.^714285714285714285) and so on for cn variable factor

∈3⅄2Qn4 of ∈1⅄1Qn and ∈2⅄1Qn variables is 

(1⅄1Qn4c1/2⅄1Qn4c1)=(1.^571428/0.^63)

(1⅄1Qn4c1/2⅄1Qn4c2)=(1.^571428/0.^6363)

(1⅄1Qn4c2/2⅄1Qn4c1)=(1.^571428571428/0.^63)

(1⅄1Qn4c3/2⅄1Qn4c2)=(1.^571428571428571428/0.^6363)

(1⅄1Qn4c2/2⅄1Qn4c3)=(1.^571428571428/0.^636363)

(1⅄1Qn4c3/2⅄1Qn4c1)=(1.^571428571428571428/0.^63)

(1⅄1Qn4c1/2⅄1Qn4c3)=(1.^571428/0.^636363) and so on for cn variable factor

∈3⅄2Qn5 of ∈1⅄1Qn and ∈2⅄1Qn variables is 

(1⅄1Qn5c1/2⅄1Qn5c1)=(1.^18/0.^846153)

(1⅄1Qn5c1/2⅄1Qn5c2)=(1.^18/0.^846153846153)

(1⅄1Qn5c2/2⅄1Qn5c1)=(1.^1818/0.^846153) and so on for cn variable factor

∈3⅄2Qn6 of ∈1⅄1Qn and ∈2⅄1Qn variables is 

(1⅄1Qn6c1/2⅄1Qn6c1)=(1.^307692/0.^7647058823529411)

(1⅄1Qn6c1/2⅄1Qn6c2)=(1.^307692/0.^76470588235294117647058823529411)

(1⅄1Qn6c2/2⅄1Qn6c1)=(1.^307692307692/0.^7647058823529411) and so on for cn variable factor

∈3⅄2Qn7 of ∈1⅄1Qn and ∈2⅄1Qn variables is 

(1⅄1Qn7c1/2⅄1Qn7c1)=(1.^1176470588235294/0.^894736842105263157)

(1⅄1Qn7c1/2⅄1Qn7c2)=(1.^1176470588235294/0.^894736842105263157894736842105263157)

(1⅄1Qn7c2/2⅄1Qn7c1)=(1.^11764705882352941176470588235294/0.^894736842105263157) and so on for cn variable factor

∈3⅄2Qn8 of ∈1⅄1Qn and ∈2⅄1Qn variables is 

(1⅄1Qn8c1/2⅄1Qn8c1)=(1.^210526315789473684/0.^8260869565217391304347)

(1⅄1Qn8c1/2⅄1Qn8c2)=(1.^210526315789473684/0.^82608695652173913043478260869565217391304347)

(1⅄1Qn8c2/2⅄1Qn8c1)=(1.^210526315789473684210526315789473684/0.^8260869565217391304347) and so on for cn variable factor

Beginning with

∈3⅄2Qn1 of ∈2⅄1Qn and ∈1⅄1Qn variables is (2⅄1Qn1cn/1⅄1Qn2cn) depending of cn variable factor

∈3⅄2Qn1 of ∈2⅄1Qn and ∈1⅄1Qn variables is 

(2⅄1Qn1c1/1⅄1Qn1c1)=(0.^6/1.5)

(2⅄1Qn1c2/1⅄1Qn1c1)=(0.^66/1.5)

(2⅄1Qn1c3/1⅄1Qn1c1)=(0.^666/1.5) and so on for cn variable factor

∈3⅄2Qn2 of ∈2⅄1Qn and ∈1⅄1Qn variables is 

(2⅄1Qn2c1/1⅄1Qn2c1)=(0.6/1.^6)

(2⅄1Qn2c1/1⅄1Qn2c2)=(0.6/1.^66)

(2⅄1Qn2c1/1⅄1Qn2c3)=(0.6/1.^666) and so on for cn variable factor

∈3⅄2Qn3 of ∈2⅄1Qn and ∈1⅄1Qn variables is 

(2⅄1Qn3c1/1⅄1Qn3c1)=(0.^714285/1.4)

(2⅄1Qn3c2/1⅄1Qn3c1)=(0.^714285714285/1.4)

(2⅄1Qn3c3/1⅄1Qn3c1)=(0.^714285714285714285/1.4) and so on for cn variable factor

∈3⅄2Qn4 of ∈2⅄1Qn and ∈1⅄1Qn variables is 

(2⅄1Qn4c1/1⅄1Qn4c1)=(0.^63/1.^571428)

(2⅄1Qn4c1/1⅄1Qn4c2)=(0.^63/1.^571428571428)

(2⅄1Qn4c2/1⅄1Qn4c1)=(0.^6363/1.^571428)

(2⅄1Qn4c3/1⅄1Qn4c2)=(0.^636363/1.^571428571428)

(2⅄1Qn4c2/1⅄1Qn4c3)=(0.^6363/1.^571428571428571428)

(2⅄1Qn4c3/1⅄1Qn4c1)=(0.^636363/1.^571428)

(2⅄1Qn4c1/1⅄1Qn4c3)=(0.^63/1.^571428571428571428) and so on for cn variable factor

∈3⅄2Qn5 of ∈2⅄1Qn and ∈1⅄1Qn variables is 

(2⅄1Qn5c1/1⅄1Qn5c1)=(0.^846153/1.^18)

(2⅄1Qn5c1/1⅄1Qn5c2)=(0.^846153/1.^1818)

(2⅄1Qn5c2/1⅄1Qn5c1)=(0.^846153846153/1.^18) and so on for cn variable factor

∈3⅄2Qn6 of ∈2⅄1Qn and ∈1⅄1Qn variables is 

(2⅄1Qn6c1/1⅄1Qn6c1)=(0.^7647058823529411/1.^307692)

(2⅄1Qn6c1/1⅄1Qn6c2)=(0.^7647058823529411/1.^307692307692)

(2⅄1Qn6c2/1⅄1Qn6c1)=(0.^76470588235294117647058823529411/1.^307692) and so on for cn variable factor

∈3⅄2Qn7 of ∈2⅄1Qn and ∈1⅄1Qn variables is 

(2⅄1Qn7c1/1⅄1Qn7c1)=(0.^894736842105263157/1.^1176470588235294)

(2⅄1Qn7c1/1⅄1Qn7c2)=(0.^894736842105263157/1.^11764705882352941176470588235294)

(2⅄1Qn7c2/1⅄1Qn7c1)=(0.^894736842105263157894736842105263157/1.^1176470588235294) and so on for cn variable factor

∈3⅄2Qn8 of ∈2⅄1Qn and ∈1⅄1Qn variables is 

(2⅄1Qn8c1/1⅄1Qn8c1)=(0.^8260869565217391304347/1.^210526315789473684)

(2⅄1Qn8c1/1⅄1Qn8c2)=(0.^8260869565217391304347/1.^210526315789473684210526315789473684)

(2⅄1Qn8c2/1⅄1Qn8c1)=(0.^82608695652173913043478260869565217391304347/1.^210526315789473684) and so on for cn variable factor



Potential Path functions of variables 1⅄Qn and 2⅄Qn


n⅄ncn(Qn)(2)=(Qn)x(Qn)

n⅄ncn(Qn)(3)=(Qn)x(Qn)x(Qn)

n⅄ncn(Qn)(4)=(Qn)x(Qn)x(Qn)x(Qn)


∈1⅄ᐱ(Q)

∈1⅄ᐱ(Qn2/An1), ∈1⅄ᐱ(Qn2/Bn1), ∈1⅄ᐱ(Qn2/Dn1), ∈1⅄ᐱ(Qn2/En1), ∈1⅄ᐱ(Qn2/Fn1), ∈1⅄ᐱ(Qn2/Gn1), ∈1⅄ᐱ(Qn2/Hn1), ∈1⅄ᐱ(Qn2/In1), ∈1⅄ᐱ(Qn2/Jn1), ∈1⅄ᐱ(Qn2/Kn1), ∈1⅄ᐱ(Qn2/Ln1), ∈1⅄ᐱ(Qn2/Mn1), ∈1⅄ᐱ(Qn2/Nn1), ∈1⅄ᐱ(Qn2/On1), ∈1⅄ᐱ(Qn2/Pn1), ∈1⅄ᐱ(Qn2/Qn1), ∈1⅄ᐱ(Qn2/Rn1), ∈1⅄ᐱ(Qn2/Sn1), ∈1⅄ᐱ(Qn2/Tn1), ∈1⅄ᐱ(Qn2/Un1),  ∈1⅄ᐱ(Qn2/Vn1), ∈1⅄ᐱ(Qn2/Wn1), ∈1⅄ᐱ(Qn2/Yn1), ∈1⅄ᐱ(Qn2/Zn1), ∈1⅄ᐱ(Qn2/φn1), ∈1⅄ᐱ(Qn2/Θn1), ∈1⅄ᐱ(Qn2/Ψn1), ∈1⅄ᐱ(Qn2cn/ᐱn1cn), ∈1⅄ᐱ(Qn2cn/ᗑn1cn), ∈1⅄ᐱ(Qn1cn/∘⧊°n1cn), ∈1⅄ᐱ(Qn2cn/∘∇°n1cn)


∈2⅄ᐱ(Q)

∈2⅄ᐱ(Qn1/An2), ∈2⅄ᐱ(Qn1/Bn2), ∈2⅄ᐱ(Qn1/Dn2), ∈2⅄ᐱ(Qn1/En2), ∈2⅄ᐱ(Qn1/Fn2), ∈2⅄ᐱ(Qn1/Gn2), ∈2⅄ᐱ(Qn1/Hn2), ∈2⅄ᐱ(Qn1/In2), ∈2⅄ᐱ(Qn1/Jn2), ∈2⅄ᐱ(Qn1/Kn2), ∈2⅄ᐱ(Qn1/Ln2), ∈2⅄ᐱ(Qn1/Mn2), ∈2⅄ᐱ(Qn1/Nn2), ∈2⅄ᐱ(Qn1/On2), ∈2⅄ᐱ(Qn1/Pn2), ∈2⅄ᐱ(Qn1/Qn2), ∈2⅄ᐱ(Qn1/Rn2), ∈2⅄ᐱ(Qn1/Sn2), ∈2⅄ᐱ(Qn1/Tn2),∈2⅄ᐱ(Qn1/Un2),  ∈2⅄ᐱ(Qn1/Vn2), ∈2⅄ᐱ(Qn1/Wn2), ∈2⅄ᐱ(Qn1/Yn2), ∈2⅄ᐱ(Qn1/Zn2), ∈2⅄ᐱ(Qn1/φn2), ∈2⅄ᐱ(Qn1/Θn2), ∈2⅄ᐱ(Qn1/Ψn2), ∈2⅄ᐱ(Qn1cn/ᐱn2cn), ∈2⅄ᐱ(Qn1cn/ᗑn2cn), ∈2⅄ᐱ(Qn1cn/∘⧊°n2cn), ∈2⅄ᐱ(Qn1cn/∘∇°n2cn)


∈3⅄ᐱ(Q)

∈3⅄ᐱ(Qncn/Ancn), ∈3⅄ᐱ(Qncn/Bncn), ∈3⅄ᐱ(Qncn/Dncn), ∈3⅄ᐱ(Qncn/Encn), ∈3⅄ᐱ(Qncn/Fncn), ∈3⅄ᐱ(Qncn/Gncn), ∈3⅄ᐱ(Qncn/Hncn), ∈3⅄ᐱ(Qncn/Incn), ∈3⅄ᐱ(Qncn/Jncn), ∈3⅄ᐱ(Qncn/Kncn), ∈3⅄ᐱ(Qncn/Lncn), ∈3⅄ᐱ(Qncn/Mncn), ∈3⅄ᐱ(Qncn/Nncn), ∈3⅄ᐱ(Qncn/Oncn), ∈3⅄ᐱ(Qncn/Pncn), ∈3⅄ᐱ(Qncn/Qncn), ∈3⅄ᐱ(Qncn/Rncn), ∈3⅄ᐱ(Qncn/Sncn), ∈3⅄ᐱ(Qncn/Tncn),∈3⅄ᐱ(Qncn/Uncn),  ∈3⅄ᐱ(Qncn/Vncn), ∈3⅄ᐱ(Qncn/Wncn), ∈3⅄ᐱ(Qncn/Yncn), ∈3⅄ᐱ(Qncn/Zncn), ∈3⅄ᐱ(Qncn/φncn), ∈3⅄ᐱ(Qncn/Θncn), ∈3⅄ᐱ(Qncn/Ψncn), ∈3⅄ᐱ(Qncn/ᐱncn), ∈3⅄ᐱ(Qncn/ᗑncn), ∈3⅄ᐱ(Qncn/∘⧊°ncn), ∈3⅄ᐱ(Qncn/∘∇°ncn)


∈n⅄Xᐱ(Q)

∈n⅄Xᐱ(QnxAn), ∈n⅄Xᐱ(QnxBn), ∈n⅄Xᐱ(QnxDn), ∈n⅄Xᐱ(QnxEn), ∈n⅄Xᐱ(QnxFn), ∈n⅄Xᐱ(QnxGn), ∈n⅄Xᐱ(QnxHn), ∈n⅄Xᐱ(QnxIn), ∈n⅄Xᐱ(QnxJn), ∈n⅄Xᐱ(QnxKn), ∈n⅄Xᐱ(QnxLn), ∈n⅄Xᐱ(QnxMn), ∈n⅄Xᐱ(QnxNn), ∈n⅄Xᐱ(QnxOn), ∈n⅄Xᐱ(QnxPn), ∈n⅄Xᐱ(QnxQn), ∈n⅄Xᐱ(QnxRn), ∈n⅄Xᐱ(QnxSn), ∈n⅄Xᐱ(QnxTn),∈n⅄Xᐱ(QnxUn),  ∈n⅄Xᐱ(QnxVn), ∈n⅄Xᐱ(QnxWn), ∈n⅄Xᐱ(QnxYn), ∈n⅄Xᐱ(QnxZn), ∈n⅄Xᐱ(Qnxφn), ∈n⅄Xᐱ(QnxΘn), ∈n⅄Xᐱ(QnxΨn), ∈n⅄Xᐱ(Qncnxᐱncn), ∈n⅄Xᐱ(Qncnxᗑncn), ∈n⅄Xᐱ(Qncnx∘⧊°ncn), ∈n⅄Xᐱ(Qncnx∘∇°ncn)


∈n+⅄ᐱ(Q

∈n+⅄ᐱ(Qn+An), ∈n+⅄ᐱ(Qn+Bn), ∈n+⅄ᐱ(Qn+Dn), ∈n+⅄ᐱ(Qn+En), ∈n+⅄ᐱ(Qn+Fn), ∈n+⅄ᐱ(Qn+Gn), ∈n+⅄ᐱ(Qn+Hn), ∈n+⅄ᐱ(Qn+In), ∈n+⅄ᐱ(Qn+Jn), ∈n+⅄ᐱ(Qn+Kn), ∈n+⅄ᐱ(Qn+Ln), ∈n+⅄ᐱ(Qn+Mn), ∈n+⅄ᐱ(Qn+Nn), ∈n+⅄ᐱ(Qn+On), ∈n+⅄ᐱ(Qn+Pn), ∈n+⅄ᐱ(Qn+Qn), ∈n+⅄ᐱ(Qn+Rn), ∈n+⅄ᐱ(Qn+Sn), ∈n+⅄ᐱ(Qn+Tn),∈n+⅄ᐱ(Qn+Un),  ∈n+⅄ᐱ(Qn+Vn), ∈n+⅄ᐱ(Qn+Wn), ∈n+⅄ᐱ(Qn+Yn), ∈n+⅄ᐱ(Qn+Zn), ∈n+⅄ᐱ(Qn+φn), ∈n+⅄ᐱ(Qn+Θn), ∈n+⅄ᐱ(Qn+Ψn), ∈n+⅄ᐱ(Qncn+ᐱncn), ∈n+⅄ᐱ(Qncn+ᗑncn), ∈n+⅄ᐱ(Qncn+∘⧊°ncn), ∈n+⅄ᐱ(Qncn+∘∇°ncn)


∈1-⅄ᐱ(Q)

∈1-⅄ᐱ(Qn2-An1), ∈1-⅄ᐱ(Qn2-Bn1), ∈1-⅄ᐱ(Qn2-Dn1), ∈1-⅄ᐱ(Qn2-En1), ∈1-⅄ᐱ(Qn2-Fn1), ∈1-⅄ᐱ(Qn2-Gn1), ∈1-⅄ᐱ(Qn2-Hn1), ∈1-⅄ᐱ(Qn2-In1), ∈1-⅄ᐱ(Qn2-Jn1), ∈1-⅄ᐱ(Qn2-Kn1), ∈1-⅄ᐱ(Qn2-Ln1), ∈1-⅄ᐱ(Qn2-Mn1), ∈1-⅄ᐱ(Qn2-Nn1), ∈1-⅄ᐱ(Qn2-On1), ∈1-⅄ᐱ(Qn2-Pn1), ∈1-⅄ᐱ(Qn2-Qn1), ∈1-⅄ᐱ(Qn2-Rn1), ∈1-⅄ᐱ(Qn2-Sn1), ∈1-⅄ᐱ(Qn2-Tn1), ∈1-⅄ᐱ(Qn2-Un1),  ∈1-⅄ᐱ(Qn2-Vn1), ∈1-⅄ᐱ(Qn2-Wn1), ∈1-⅄ᐱ(Qn2-Yn1), ∈1-⅄ᐱ(Qn2-Zn1), ∈1-⅄ᐱ(Qn2-φn1), ∈1-⅄ᐱ(Qn2-Θn1), ∈1-⅄ᐱ(Qn2-Ψn1), ∈1-⅄ᐱ(Qn2cn-ᐱn1cn), ∈1-⅄ᐱ(Qn2cn-ᗑn1cn), ∈1-⅄ᐱ(Qn1cn-∘⧊°n1cn), ∈1-⅄ᐱ(Qn2cn-∘∇°n1cn)


∈2-⅄ᐱ(Q)

∈2-⅄ᐱ(Qn1-An2), ∈2-⅄ᐱ(Qn1-Bn2), ∈2-⅄ᐱ(Qn1-Dn2), ∈2-⅄ᐱ(Qn1-En2), ∈2-⅄ᐱ(Qn1-Fn2), ∈2-⅄ᐱ(Qn1-Gn2), ∈2-⅄ᐱ(Qn1-Hn2), ∈2-⅄ᐱ(Qn1-In2), ∈2-⅄ᐱ(Qn1-Jn2), ∈2-⅄ᐱ(Qn1-Kn2), ∈2-⅄ᐱ(Qn1-Ln2), ∈2-⅄ᐱ(Qn1-Mn2), ∈2-⅄ᐱ(Qn1-Nn2), ∈2-⅄ᐱ(Qn1-On2), ∈2-⅄ᐱ(Qn1-Pn2), ∈2-⅄ᐱ(Qn1-Qn2), ∈2-⅄ᐱ(Qn1-Rn2), ∈2-⅄ᐱ(Qn1-Sn2), ∈2-⅄ᐱ(Qn1-Tn2), ∈2-⅄ᐱ(Qn1-Un2),  ∈2-⅄ᐱ(Qn1-Vn2), ∈2-⅄ᐱ(Qn1-Wn2), ∈2-⅄ᐱ(Qn1-Yn2), ∈2-⅄ᐱ(Qn1-Zn2), ∈2-⅄ᐱ(Qn1-φn2), ∈2-⅄ᐱ(Qn1-Θn2), ∈2-⅄ᐱ(Qn1-Ψn2), ∈2-⅄ᐱ(Qn1cn-ᐱn2cn), ∈2-⅄ᐱ(Qn1cn-ᗑn2cn), ∈2-⅄ᐱ(Qn1cn-∘⧊°n2cn), ∈2-⅄ᐱ(Qn1cn-∘∇°n2cn)


∈3-⅄ᐱ(nQncn)

∈3-⅄ᐱ(Qncn-Ancn), ∈3-⅄ᐱ(Qncn-Bncn), ∈3-⅄ᐱ(Qncn-Dncn), ∈3-⅄ᐱ(Qncn-Encn), ∈3-⅄ᐱ(Qncn-Fncn), ∈3-⅄ᐱ(Qncn-Gncn), ∈3-⅄ᐱ(Qncn-Hncn), ∈3-⅄ᐱ(Qncn-Incn), ∈3-⅄ᐱ(Qncn-Jncn), ∈3-⅄ᐱ(Qncn-Kncn), ∈3-⅄ᐱ(Qncn-Lncn), ∈3-⅄ᐱ(Qncn-Mncn), ∈3-⅄ᐱ(Qncn-Nncn), ∈3-⅄ᐱ(Qncn-Oncn), ∈3-⅄ᐱ(Qncn-Pncn), ∈3-⅄ᐱ(Qncn-Qncn), ∈3-⅄ᐱ(Qncn-Rncn), ∈3-⅄ᐱ(Qncn-Sncn), ∈3-⅄ᐱ(Qncn-Tncn), ∈3-⅄ᐱ(Qncn-Uncn),  ∈3-⅄ᐱ(Qncn-Vncn), ∈3-⅄ᐱ(Qncn-Wncn), ∈3-⅄ᐱ(Qncn-Yncn), ∈3-⅄ᐱ(Qncn-Zncn), ∈3-⅄ᐱ(Qncn-φncn), ∈3-⅄ᐱ(Qncn-Θncn), ∈3-⅄ᐱ(Qncn-Ψncn), ∈3-⅄ᐱ(Qncn-ᐱncn), ∈3-⅄ᐱ(Qncn-ᗑncn), ∈3-⅄ᐱ(Qncn-∘⧊°ncn), ∈3-⅄ᐱ(Qncn-∘∇°ncn)


And functions Q quotients of P prime consecutive variables as second factor in equation paths with a Number nNncn

∈n⅄X(nNncnxn⅄nQncn) and ∈n⅄X(nAncnxn⅄nQncn) through ∈n⅄X(nZncnxn⅄nQncn) and ∈n⅄X(nφncnxn⅄nQncn), ∈n⅄X(nΘncnxn⅄nQncn), ∈n⅄X(nΨncnxn⅄nQncn) . . . and so on.

∈n⅄(nNncn/n⅄nQncn) and ∈n⅄(nAncn/n⅄nQncn) through ∈n⅄(nZncn/n⅄nQncn) and ∈n⅄(nφncn/n⅄nQncn), ∈n⅄(nΘncn/n⅄nQncn), ∈n⅄(nΨncn/n⅄nQncn) . . . and so on.

∈n+⅄(nNncn+n⅄nQncn) and ∈n+⅄(nAncn+n⅄nQncn) through ∈n+⅄(nZncn+n⅄nQncn) and ∈n+⅄(nφncn+n⅄nQncn), ∈n+⅄(nΘncn+n⅄nQncn), ∈n+⅄(nΨncn+n⅄nQncn) . . and so on.

∈n-⅄(nNncn-n⅄nQncn) and ∈n-⅄(nAncn-n⅄nQncn) through ∈n-⅄(nZncn-n⅄nQncn) and ∈n-⅄(nφncn-n⅄nQncn), ∈n-⅄(nΘncn-n⅄nQncn), ∈n-⅄(nΨncn-n⅄nQncn) . . . and so on.



n⅄∀n(NncnxnQncn), n⅄∀n(Nncn/nQncn), n⅄∀n(Nncn+nQncn), and n⅄∀n(Nncn-nQncn) functions for all or for any variables of sequential variables in sets of prime quotient variable functions of complex values n⅄ncn(nQncn)(n) determined on cn definition in the ratios.

if you need a 1dir 2dir to 3dir

email@1dir.cc

c.dir.1dir.cc  c.dir.1dir.org  c.dir.1dir.cloud

c://dir