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Since we have also defined xE# (Extended Hyper-E Notation), let's go on to forge some even bigger numbers in this system! In this article I will introduce some additional regiments (with more extension!). In Saibian's original list, it covers googolism's 1142 through 2684. That's 1543 new googolism's. In addition there are 12 additional googolism's introduced as early betas of the Cascading-E Numbers! Let's get started...
First, let's start with the first super regiment, called "gugold super regiment"!
GUGOLD SUPER REGIMENT
GUGOLD SUPER REGIMENT
Categories 11 - 20
Regiment blocks 13 - 23
Members: 773 (130 original + 643 new)
Gugold regiment
Gugold regiment
Category 11
Regiment block 13
Members: 222 (13 original + 209 new) [more and more]
(2297 - 2518)
[FGH level ω => ω+1]
Level 1 | Stage 3-1
Stage 3-1 ~ Breaking the primitive recursive function level
Now we are going to jump ahead to some really big numbers. Imagine that E100 (googol) is stage 1, E100#100 (grangol) is stage 2, E100#100#100 (greagol) is stage 3, E100#100#100#100 (gigangol) is stage 4, E100#100#100#100#100 (gorgegol) is stage 5, E100#100#100#100#100#100 (gulgol) is stage 6, E100#100#100#100#100#100#100 (gaspgol) is stage 7, E100#100#100#100#100#100#100#100 (ginorgol) is stage 8, E100#100#100#100#100#100#100#100#100 (gargantuul) is stage 9, E100#100#100#100#100#100#100#100#100#100 (googondol) is stage 10 ... now imagine this were to continue with a 11th-gol, 12th-gol, 13th-gol, 14th-gol ...
Now let's call the 100th-gol as "gugold" (short for the "golden googol", formerly called "goolda"). So...
(2297) gugold ☆★✪ = E100#100#100#100# ... ... ... ... #100#100#100#100 (w/100 100s)
This expands:
E100#100#100#100#100#100#100#100#100#100#
100#100#100#100#100#100#100#100#100#100#
100#100#100#100#100#100#100#100#100#100#
100#100#100#100#100#100#100#100#100#100#
100#100#100#100#100#100#100#100#100#100#
100#100#100#100#100#100#100#100#100#100#
100#100#100#100#100#100#100#100#100#100#
100#100#100#100#100#100#100#100#100#100#
100#100#100#100#100#100#100#100#100#100
This can also be written more compactly using Extended Hyper-E notation as:
gugold = E100##100
*alternatively, It can also be called (2298) gugond
This brings me to the limits of poly-cell notation. Remember however, that even as a kid I had speculated going beyond this. If I could imagine a number with a hundred cells, then I could imagine a number with THAT number of cells. So now let us define the following:
(2299) gugolda-suplex ☆★ = E100##100#2 = E100##(E100##100)
= E100#100#100# ... ... ... ... ... ... ... ... #100#100#100 (w/ gugold 100s)
*also called (2300) gugonda-suplex
(2301) gugolda-dusuplex ☆ = E100##100#3 = E100##(E100##2)
= E100#100# ... ... ... ... ... ... ... ... ... ... #100#100 (w/ gugolda-suplex 100s)
*also called (2302) gugonda-dusuplex
Saibian however, he conclude that he doesn't define some continuations of E100##100#n for n > 3, in the simplest case, gugolda-trisuplex = E100##100#4.
So, to continue, I have to think something beyond E100##100#3! We call it gugolda-trisuplex! Say,
(2303) gugolda-trisuplex ☆ = E100##100#4 = E100##(E100##100#3)
But why I am not done yet. Let's continue even further with -quadrisuplex, -quintisuplex, -sextisuplex, and so on...
(2304) gugolda-quadrisuplex = E100##100#5
(2305) gugolda-quintisuplex = E100##100#6
(2306) gugolda-sextisuplex = E100##100#7
(2307) gugolda-septisuplex = E100##100#8
(2308) gugolda-octisuplex = E100##100#9
(2309) gugolda-nonisuplex = E100##100#10
(2310) gugolda-decisuplex = E100##100#11
...
(2311) gugolda-undecisuplex = E100##100#12
(2312) gugolda-duodecisuplex = E100##100#13
(2313) gugolda-tredecisuplex = E100##100#14
(2314) gugolda-quattuordecisuplex = E100##100#15
(2315) gugolda-quindecisuplex = E100##100#16
(2316) gugolda-sexdecisuplex = E100##100#17
(2317) gugolda-septendecisuplex = E100##100#18
(2318) gugolda-octodecisuplex = E100##100#19
(2319) gugolda-novemdecisuplex = E100##100#20
(2320) gugolda-vigintisuplex = E100##100#21
...
(2321) gugolda-unvigintisuplex = E100##100#22
(2322) gugolda-duovigintisuplex = E100##100#23
(2323) gugolda-trevigintisuplex = E100##100#24
(2324) gugolda-quattuorvigintisuplex = E100##100#25
(2325) gugolda-quinvigintisuplex = E100##100#26
(2326) gugolda-sexvigintisuplex = E100##100#27
(2327) gugolda-septenvigintisuplex = E100##100#28
(2328) gugolda-octovigintisuplex = E100##100#29
(2329) gugolda-novemvigintisuplex = E100##100#30
...
(2330) gugolda-trigintisuplex = E100##100#31
(2331) gugolda-quadragintisuplex = E100##100#41
(2332) gugolda-quinquagintisuplex = E100##100#51
(2333) gugolda-sexagintisuplex = E100##100#61
(2334) gugolda-septuagintisuplex = E100##100#71
(2335) gugolda-octogintisuplex = E100##100#81
(2336) gugolda-nonagintisuplex = E100##100#91
...
(2337) gugolda-centisuplex = E100##100#101
(2338) gugolda-ducentisuplex = E100##100#201
(2339) gugolda-trecentisuplex = E100##100#301
(2340) gugolda-quadringentisuplex = E100##100#401
(2341) gugolda-quingentisuplex = E100##100#501
(2342) gugolda-sescentisuplex = E100##100#601
(2343) gugolda-septingentisuplex = E100##100#701
(2344) gugolda-octingentisuplex = E100##100#801
(2345) gugolda-nongentisuplex = E100##100#901
...
(2346) gugolda-millisuplex = E100##100#1001
(2347) gugolda-decimillisuplex = E100##100#10,001
(2348) gugolda-centimillisuplex = E100##100#100,001
(2349) gugolda-milli-millisuplex = E100##100#1,000,001
To get even more googolism's in the regiment we can apply some of the argument-modifiers. These modifiers never get outdated because they adjust to whatever growth rate we are considering and only change the argument. First, we will use chime, toll, and gong...
(2350) gugoldachime = E1000##1000
(2351) gugolda-suplexichime = E1000##1000#2
(2352) gugolda-dusuplexichime = E1000##1000#3
(2353) gugolda-trisuplexichime = E1000##1000#4
(2354) gugolda-quadrisuplexichime = E1000##1000#5
(2355) gugolda-quintisuplexichime = E1000##1000#6
...
(2356) gugoldatoll = E10,000##10,000
(2357) gugolda-suplexitoll = E10,000##10,000#2
(2358) gugolda-dusuplexitoll = E10,000##10,000#3
(2359) gugolda-trisuplexitoll = E10,000##10,000#4
(2360) gugolda-quadrisuplexitoll = E10,000##10,000#5
(2361) gugolda-quintisuplexitoll = E10,000##10,000#6
...
This brings us to the gugoldagong. Now here is a number that really leaves the googolgong in the dust!
Say,
googolgong = E100,000 = 10^100,000
grangolgong = E100,000#100,000
greagolgong = E100,000#100,000#100,000
then...
(2362) gugoldagong ☆ = E100,000##100,000
= E100,000#100,000#100,000# ... ... ... ... ... ... #100,000#100,000#100,000 (w/ 100,000 100,000's)
(2363) gugolda-suplexigong = E100,000##100,000#2
(2364) gugolda-dusuplexigong = E100,000##100,000#3
(2365) gugolda-trisuplexigong = E100,000##100,000#4
(2366) gugolda-quadrisuplexigong = E100,000##100,000#5
(2367) gugolda-quintisuplexigong = E100,000##100,000#6
(2368) gugolda-sextisuplexigong = E100,000##100,000#7
(2369) gugolda-septisuplexigong = E100,000##100,000#8
(2370) gugolda-octisuplexigong = E100,000##100,000#9
(2371) gugolda-nonisuplexigong = E100,000##100,000#10
(2372) gugolda-decisuplexigong = E100,000##100,000#11
...
(2373) gugolda-vigintisuplexigong = E100,000##100,000#21
(2374) gugolda-centisuplexigong = E100,000##100,000#101
(2375) gugolda-millisuplexigong = E100,000##100,000#1001
(2376) gugolda-milli-millisuplexigong = E100,000##100,000#1,000,001
Furthermore, Saibian missed some existing argument modifiers like -ding, -bell, -bong, -throng, -gandingan, etc. So, I made up here to fill some even more naming gaps.
(2377) gugoldading = E500##500
(2378) gugolda-suplexiding = E500##500#2
(2379) gugolda-dusuplexiding = E500##500#3
...
(2380) gugoldabell = E5000##5000
(2381) gugolda-suplexibell = E5000##5000#2
(2382) gugolda-dusuplexibell = E5000##5000#3
...
(2383) gugoldabong = E100,000,000##100,000,000
(2384) gugolda-suplexibong = E100,000,000##100,000,000#2
(2385) gugolda-dusuplexibong = E100,000,000##100,000,000#3
...
(2386) gugoldathrong = E100,000,000,000##100,000,000,000
(2387) gugolda-suplexithrong = E100,000,000,000##100,000,000,000#2
(2388) gugolda-dusuplexithrong = E100,000,000,000##100,000,000,000#3
...
(2389) gugoldagandingan = E100,000,000,000,000##100,000,000,000,000
(2390) gugolda-suplexigandingan = E100,000,000,000,000##100,000,000,000,000#2
(2391) gugolda-dusuplexigandingan = E100,000,000,000,000##100,000,000,000,000#3
...
What is more? Let's start to coin an irregular googolism that is so close to some famous googolism. We coin something very close to "Little Graham". Say,
Little Graham ~ E3##12#7
then we have...
(2392) Squeaker Graham ☆ = E[2]3##12#7
Here is a visual representation of Squeaker Graham:
Though, the name seems to be simply inspired by the former smaller googolism called "little squeaker" in the guppy regiment, as...
(6) little squeaker = 5E10 = 5*10^10 = 50,000,000,000
Due to the size of the series, hence the loan name.
I am not done with this yet. I am going to make n-ary versions of gugold as follows:
(2393) gugoldabit = E[2]100##100
*also called (2394) binary-gugold
(2395) ternary-gugold = E[3]100##100
(2396) quaternary-gugold = E[4]100##100
(2397) quinary-gugold = E[5]100##100
(2398) senary-gugold = E[6]100##100
(2399) gugoldabyte = E[8]100##100
*also called (2400) octal-gugold
(2401) duodecimal-gugold = E[12]100##100
(2402) hexadecimal-gugold = E[16]100##100
(2403) vigesimal-gugold = E[20]100##100
(2404) sexagesimal-gugold = E[60]100##100
And some in-between numbers in the regiment, using -suplex suffix...
(2405) googolsuplex ☆ = E100##1#2 = E100##(E100)
*also (2283) great googol
(2406) grangolsuplex = E100##2#2 = E100##(E100#100)
*also (2284) great grangol
(2407) greagolsuplex = E100##3#2 = E100##(E100#100#100)
*also (2285) great greagol
(2408) gigangolsuplex = E100##4#2 = E100##(E100#100#100#100)
*also (2286) great gigangol
(2409) gorgegolsuplex = E100##5#2
*also (2287) great gorgegol
(2410) gulgolsuplex = E100##6#2
*also (2288) great gulgol
(2411) gaspgolsuplex = E100##7#2
*also (2289) great gaspgol
(2412) ginorgolsuplex = E100##8#2
*also (2290) great ginorgol
(2413) gargantuulsuplex = E100##9#2
*also (2291) great gargantuul
(2414) googondolsuplex = E100##10#2
*also (2292) great googondol
...
(2415) googonkosolsuplex = E100##20#2
*also (2293) great googonkosol
(2416) googonhectolsuplex = E100##100#2
*also (2294) great googonhectol
(2417) googonchiliolsuplex = E100##1000#2
*also (2295) great googonchiliol
(2418) googonmyriolsuplex = E100##10,000#2
*also (2296) great googonmyriol
We can also introduce the "grand" operator in the similar fashion to gugolda-suplex. However, Saibian originally introduced the "grand" operator at throogol.
(2419) grand gugold = E100##100#2
(2420) grand grand gugold = E100##100#3
(2421) grand grand grand gugold = E100##100#4
*also called (2422) three-ex-grand gugold
(2423) grand grand grand grand gugold = E100##100#5
*also called (2424) four-ex-grand gugold
(2425) five-ex-grand gugold = E100##100#6
(2426) six-ex-grand gugold = E100##100#7
(2427) seven-ex-grand gugold = E100##100#8
(2428) eight-ex-grand gugold = E100##100#9
(2429) nine-ex-grand gugold = E100##100#10
(2430) ten-ex-grand gugold = E100##100#11
...
(2432) twenty-ex-grand gugold = E100##100#21
...
(2433) hundred-ex-grand gugold = E100##100#101
(2434) thousand-ex-grand gugold = E100##100#1001
(2435) ten thousand-ex-grand gugold = E100##100#10,001
(2436) hundred thousand-ex-grand gugold = E100##100#100,001
(2437) million-ex-grand gugold = E100##100#1,000,001
(2438) billion-ex-grand gugold = E100##100#1,000,000,001
(2439) trillion-ex-grand gugold = E100##100#1,000,000,000,001
(2440) quadrillion-ex-grand gugold = E100##100#(10^15+1)
(2441) quintillion-ex-grand gugold = E100##100#(10^18+1)
(2442) sextillion-ex-grand gugold = E100##100#(10^21+1)
(2443) septillion-ex-grand gugold = E100##100#(10^24+1)
(2444) octillion-ex-grand gugold = E100##100#(10^27+1)
(2445) nonillion-ex-grand gugold = E100##100#(10^30+1)
(2446) decillion-ex-grand gugold = E100##100#(10^33+1)
(2447) vigintillion-ex-grand gugold = E100##100#(10^63+1)
(2448) centillion-ex-grand gugold ✡ = E100##100#(10^303+1)
We can also introduce -dusuplex in-between googolisms like...
(2449) googoldusuplex = E100##1#3 = E100##(E100##1#2) = E100##googolsuplex
(2450) grangoldusuplex = E100##2#3
(2451) greagoldusuplex = E100##3#3
(2452) gigangoldusuplex = E100##4#3
(2453) gorgegoldusuplex = E100##5#3
(2454) gulgoldusuplex = E100##6#3
(2455) gaspgoldusuplex = E100##7#3
(2456) ginorgoldusuplex = E100##8#3
(2457) gargantuuldusuplex = E100##9#3
(2458) googondoldusuplex = E100##10#3
...
(2459) googonhectoldusuplex = E100##100#3
with -trisuplex...
(2460) googoltrisuplex = E100##1#4
(2461) grangoltrisuplex = E100##2#4
(2462) greagoltrisuplex = E100##3#4
(2463) gigangoltrisuplex = E100##4#4
(2464) gorgegoltrisuplex = E100##5#4
(2465) gulgoltrisuplex = E100##6#4
(2466) gaspgoltrisuplex = E100##7#4
(2467) ginorgoltrisuplex = E100##8#4
(2468) gargantuultrisuplex = E100##9#4
(2469) googondoltrisuplex = E100##10#4
...
with -quadrisuplex...
(2470) googolquadrisuplex = E100##1#5
(2471) grangolquadrisuplex = E100##2#5
(2472) greagolquadrisuplex = E100##3#5
(2473) gigangolquadrisuplex = E100##4#5
...
with -quintisuplex...
(2474) googolquintisuplex = E100##1#6
(2475) grangolquintisuplex = E100##2#6
(2476) greagolquintisuplex = E100##3#6
(2477) gigangolquintisuplex = E100##4#6
...
and finally, the higher n-suplexes...
(2478) googolsextisuplex = E100##1#7
(2479) googolseptisuplex = E100##1#8
(2480) googoloctisuplex = E100##1#9
(2481) googolnonisuplex = E100##1#10
(2482) googoldecisuplex = E100##1#11
We can also extend the eceton series as follows...
(2483) ecetonsuplex ☆ = E303##1#2 = E303##(E303) = E303##(10^303) = E303##centillion
(2484) ecetondusuplex = E303##1#3
(2485) ecetontrisuplex = E303##1#4
(2486) ecetonquadrisuplex = E303##1#5
(2487) ecetonquintisuplex = E303##1#6
...
(2488) eceto-grangolsuplex = E303##2#2
(2489) eceto-greagolsuplex = E303##3#2
(2490) eceto-gigangolsuplex = E303##4#2
(2491) eceto-gorgegolsuplex = E303##5#2
(2492) eceto-gulgolsuplex = E303##6#2
(2493) eceto-gaspgolsuplex = E303##7#2
(2494) eceto-ginorgolsuplex = E303##8#2
(2495) eceto-gargantuulsuplex = E303##9#2
(2496) eceto-googondolsuplex = E303##10#2
...
(2497) eceto-grangoldusuplex = E303##2#3
(2498) eceto-greagoldusuplex = E303##3#3
(2499) eceto-gigangoldusuplex = E303##4#3
...
(2500) eceto-gugold ☆ = E303##303
= E303#303#303#303# ... ... ... ... ... ... #303#303#303#303 (w/ 303 303's)
(2501) eceto-gugolda-suplex = E303##303#2
(2502) eceto-gugolda-dusuplex = E303##303#3
(2503) eceto-gugolda-trisuplex = E303##303#4
(2504) eceto-gugolda-quadrisuplex = E303##303#5
(2505) eceto-gugolda-quintisuplex = E303##303#6
Finally, we can also introduce multiple "great" operators to Hyper-E googolisms as follows...
(2506) great great googol = E100##1#3 = E100##(E100##1#2) = E100##great googol
(2507) great great grangol = E100##2#3
(2508) great great greagol = E100##3#3
(2509) great great gigangol = E100##4#3
(2510) great great gorgegol = E100##5#3
(2511) great great gulgol = E100##6#3
(2512) great great gaspgol = E100##7#3
(2513) great great ginorgol = E100##8#3
(2514) great great gargantuul = E100##9#3
(2515) great great googondol = E100##10#3
...
(2516) great great great googol = E100##1#4
*also called (2517) three-ex-great googol
(2518) great great great great googol ✡ = E100##1#5
*also called (2519) four-ex-great googol
Before we moving on graatagold regiment, let's peek on the extended guppy regiment.
Guppy regiment extended-A
Guppy regiment extended-A
Category 1
Regiment block 14
Members: 59
(2520 - 2578)
First, we can repeat the size modifiers and power modifiers into the respective googolisms.
We have:
googolspeck = E90 = 10^90
googolcrumb = E95 = 10^95
googolchunk = E99 = 10^99
googolbunch = E101 = 10^101
googolcrowd = E105 = 10^105
googolswarm = E110 = 10^110
So:
(2520) googolspeckspeck = E(100-10-10) = E80 = 10^80
(2521) googolcrumbcrumb = E(100-5-5) = E90 = 10^90
(2522) googolchunkchunk = E(100-1-1) = E98 = 10^98
(2523) googolbunchbunch = E(100+1+1) = E102 = 10^102
(2524) googolcrowdcrowd = E(100+5+5) = E110 = 10^110
(2525) googolswarmswarm = E(100+10+10) = E120 = 10^120
We can also do this with guppy = 100,000,000,000,000,000,000, using the same reasoning above. Say, we can have:
(2526) guppyspeckspeck = E0 = 1
(2527) guppycrumbcrumb = E10 = 10^10 = 10,000,000,000
(2528) guppychunkchunk = E18 = 10^18 = 1,000,000,000,000,000,000
(2529) guppybunchbunch = E22 = 10^22
(2530) guppycrowdcrowd = E30 = 10^30
(2531) guppyswarmswarm = E40 = 10^40
With power modifiers in a non-standard manner...
(2532) googoldingding = E(100*5*5) = E2500 = 10^2500
(2533) googolchimechime = E(100*10*10) = E10,000 = 10^10,000
(2534) googolbellbell = E(100*50*50) = E250,000 = 10^250,000
(2535) googoltolltoll = E(100*100*100) = E1,000,000 = 10^1,000,000
(2536) googolgonggong = E(100*1000^2) = E100,000,000 = 10^100,000,000
*also (312) googolbong
(2537) googolgonggonggong = E(100*1000^3) = E100,000,000,000 = 10^100,000,000,000
*also (313) googolthrong
(2538) googolgonggonggonggong = E(100*1000^4) = E100,000,000,000,000 = 10^100,000,000,000,000
*also (314) googolgandingan
Remember, we can also have over 10 possibilities of guppy regiment number names that equal to the same number, such as
(2539) binary-clover mite-crumb, (2540) ternary-clover mite-crumb, (2541) quaternary-clover mite-crumb, (2542) quinary-clover mite-crumb,
(2543) senary-clover mite-crumb, (2544) octal-clover mite-crumb, (2545) duodecimal-clover mite-crumb, (2546) hexadecimal clover mite-crumb,
(2547) vigesimal clover mite-crumb, and (2548) sexagesimal clover mite-crumb
= 2
This because 2*E[x](5-5) = 2*E[x]0 = 2*1 = 2 (ignoring the base)
We can also continue to construct even more complex n-plexes googolisms like:
(2549) googol-googol-ex-plex = E100#(E100+1) = E100#(googol+1)
That's larger than googoldex! Say,
googoldex = E100#1#2 = E100#(E100) = E100#googol
And something more like:
(2550) guppy-guppy-ex-plex = E20#(E20+1) = E20#(guppy+1)
Why I miss -plexiding and -plexibell? Let's coin something further!
(2551) googolplexiding = E500#2 = 10^10^500
(2552) googolduplexiding = E500#3 = 10^10^10^500
(2553) googoltriplexiding = E500#4 = 10^10^10^10^500
(2554) googolquadriplexiding = E500#5 = 10^10^10^10^10^500
(2555) googolquintiplexiding = E500#6 = 10^10^10^10^10^10^500
(2556) googolsextiplexiding = E500#7
(2557) googolseptiplexiding = E500#8
(2558) googoloctiplexiding = E500#9
(2559) googolnoniplexiding = E500#10
(2560) googoldeciplexiding = E500#11
...
(2561) googolvigintiplexiding = E500#21
(2562) googolcentiplexiding = E500#101
(2563) googolmilliplexiding = E500#1001
(2564) googolmilli-milliplexiding = E500#1,000,001
And...
(2565) googolplexibell = E5000#2 = 10^10^5000
(2566) googolduplexibell = E5000#3 = 10^10^10^5000
(2567) googoltriplexibell = E5000#4 = 10^10^10^10^5000
(2568) googolquadriplexibell = E5000#5 = 10^10^10^10^10^5000
(2569) googolquintiplexibell = E5000#6 = 10^10^10^10^10^10^5000
(2570) googolsextiplexibell = E5000#7
(2571) googolseptiplexibell = E5000#8
(2572) googoloctiplexibell = E5000#9
(2573) googolnoniplexibell = E5000#10
(2574) googoldeciplexibell = E5000#11
...
(2575) googolvigintiplexibell = E5000#21
(2576) googolcentiplexibell = E5000#101
(2577) googolmilliplexibell = E5000#1001
(2578) googolmilli-milliplexibell = E5000#1,000,001
And now, the tradition here comes to the big fix!
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