Merry Christmas 2025! I created 45 + 25 = 70 numbers to celebrate the Christmas Day 2025.
Note: The first 55 numbers are in base 607,500 (equals to 12 (meaning December) × 25 (meaning the 25th day of December) × 2025 (meaning the year 2025)).
Members: 70
Christmas's base = 607,500
Christmas's square = 369,056,250,000
Christmas's cube = 224,201,671,875,000,000
Christmas's fourth power = 136,202,515,664,062,500,000,000 = 1.362025156640625 × 10^23
Christmas's triangular number = 184,528,428,750
Christmas's base-10 exponential = 10^607,500
Christmas's base-2 exponential = 2^607,500 ≈ 5.2767420995 × 10^182,875
Christmas's base-16 exponential = 16^607,500 = 2^2,430,000 ≈ 7.752887361 × 10^731,502
Christmas's power tower = 607,500^607,500 ≈ 2.325301317 × 10^3,513,504
Christmas's factorial = 607,500! ≈ 5.748917646 × 10^3,249,673 (using Stirling's approximation)
Christmas's double power tower = 607,500^^3 = 607,500^607,500^607,500 ≈ 10^(3.087495532 × 10^3,513,504)
Christmas's triple power tower = 607,500^^4 = 607,500^607,500^607,500^607,500 ≈ 10^10^(3.087495532 × 10^3,513,504)
Christmas's quadruple power tower = 607,500^^5 = 607,500^607,500^607,500^607,500^607,500 ≈ 10^10^10^(3.087495532 × 10^3,513,504)
Christmas's quintuple power tower = 607,500^^6 = 607,500^607,500^607,500^607,500^607,500^607,500 ≈ 10^10^10^10^(3.087495532 × 10^3,513,504)
Christmas's tetration tower = 607,500^^607,500
Christmas's tetration-power tower = 607,500^^607,500^607,500
Christmas's double-tetration tower = 607,500^^607,500^^607,500 = 607,500^^^3
Christmas's triple-tetration tower = 607,500^^607,500^^607,500^^607,500 = 607,500^^^4
Christmas's pentation tower = 607,500^^^607,500
Christmas's double-pentation tower = 607,500^^^607,500^^^607,500 = 607,500^^^^3
Christmas's hexation tower = 607,500^^^^607,500
Christmas's hepation tower = 607,500^^^^^607,500
Christmas's octation tower = 607,500^^^^^^607,500
Christmas's enneation tower = 607,500^^^^^^^607,500
Christmas's decation tower = 607,500^^^^^^^^607,500
Christmas's full hyper-operator = 607,500{607,500}607,500 = 607,500^^^^^...^^^^^607,500 with 607,500 arrows
Christmas's Graham function = G(607,500) where G denotes the Graham sequence used to define Graham's number
The Christmas Tree = TREE(607,500)
Super Christmas Tree = TREE^607,500(607,500)
The Christmas SSCG-Tree = SSCG(607,500)
The Christmas SCG-Tree = SCG(607,500)
Rayo-Christmas = Rayo^{TREE(607,500)}(TREE(607,500))
Sam of Christmas = Sam(607,500)
Double Sam of Christmas = Sam(Sam(607,500))
Triple Sam of Christmas = Sam(Sam(Sam(607,500)))
Nested Sam of Christmas = Sam^607,500(607,500)
More Nested Sam of Christmas = Sam^{Sam(607,500)}(607,500)
Even More Nested Sam of Christmas = Sam^{Sam^{Sam(607,500)}(607,500)}(607,500)
Superior Sam of Christmas = Sam{1}(607,500)
Double Superior Sam of Christmas = Sam{1}^2(607,500)
Duper Superior Sam of Christmas = Sam{2}(607,500)
Truper Superior Sam of Christmas = Sam{3}(607,500)
Quadruper Superior Sam of Christmas = Sam{4}(607,500)
Ultimate Sam of Christmas = Sam{ω}(607,500)
Super Ultimate Sam of Christmas = Sam{ω^2}(607,500)
Mega Ultimate Sam of Christmas = Sam{ω^ω}(607,500)
Giga Ultimate Sam of Christmas = Sam{ω^ω^ω}(607,500)
Meta Ultimate Sam of Christmas = Sam{ε0}(607,500)
Hyper Ultimate Sam of Christmas = Sam{ω1CK}(607,500) where ω1CK denotes the Church-Kleene ordinal
Omega Ultimate Sam of Christmas = Sam{Ω}(607,500) where Ω denotes the first uncountable cardinal
Final Sam of Christmas = Sam{Indescribable cardinal}(607,500)
Christmas's Flashy-E = E[607,500]607,500#{&^&^&^#{&^(&^&&#^^#*&)}#}#607,500 in collapsing-E notation
Christmas's Weird Chain = 607,500 →{45} 607,500 →{45} 607,500 →{45} 607,500 in Peter Hurford's extension of chained arrow notation
Prickly Christmas = 607,500[0]607,500 in DeepLineMadom's array notation = 607,500 + 607,500 = 1,215,000
Dreamy Christmas = 607,500[1,1,2]607,500 in DeepLineMadom's array notation = 607,500[1,607500]607,500
All I Want for Christmas Is You = s(12, 3, 4, 5 {6} 2 {7, 8, 9} 2 {1 ` 2} 2 {1 ,, 1 {1 ,, 1 ,, 2} 2} 2) in strong array notation (*reference to a Christmas song by Mariah Carey)
Last Christmas = 768{{{{{{{{{{{{25}}}}}}}}}}}} in binary bisector notation (*reference to a Christmas song by Wham!)
Wonderful Christmastime = E[67]24#{&^&#{&^&#}##}#2025 in collapsing-E notation (*reference to a Christmas song by Paul McCartney)
Merry Christmas (Holy Elton Sheeran) = 2021{{0, 4}{{0, 4}{{0, 4}{0, 3}, 3}, 3}} (*reference to the song "Merry Christmas" by Ed Sheeran and Elton John)
Santa Tell Me = {12, 25, 2025 [1 [1 [1 \{3} 3] 2] 2] 2} in Bird's array notation (*reference to a Christmas song by Ariana Grande)
Underneath the Tree = {2025, 607500, 69420, 1337, 142857, 1, 1, 2} in BEAF/BAN (*reference to a Christmas song by Kelly Clarkson)
Santa Claus Is Comin' to Town = 1934{{1}.19 + 34}{{2}{1}{1}{1} + 7} in base-1934 bisector notation (same as binary bisector notation but n{0} = 1,934^n instead of 2^n) (*reference to a 1934 Christmas song)
Have Yourself a Merry Little Christmas = Sam{1943}(FOOT^10(10^100)) where FOOT^10(10^100) is also known as BIG FOOT (*reference to a 1943 Christmas song)
Festive Platformer (ho ho ho) = 67{{3}}12,252,025 in hyperoperator bisector notation = {67, 67, 67, 67, 12252025} in BEAF/BAN (*Not to be confused with 67{{3}}12,252,025 in Bowers' hyperoperator extension, which the latter is equal to 67{{1} + 3}12,252,025 in hyperoperator bisector notation or {67, 12252025, 3, 2} in BEAF/BAN.)
How Taylor Swift own Christmas songs? = s(1989, 36, 1225 {1 {1 {1 ` 2 ` 2`}` 2`} 2} 2) in strong array notation
Christmas Candyland of XYZ = {3, 5, 7 (0, 0, 5 (1) 1, 3, 1)(1 (1) 1, 3, 1) 2} in BEAF
50,625 Hz of Christmas, I merry you = 50,625{1}{2}{4}{{0, 2}{{0, 2}, 1}} in binary bisector notation
Vibrant epiphany of Christmas = 987,654,321{{0, 9}{0, 8}} in binary bisector notation
Nice Christmas = 69{420}{{{{0, 2}, 2}, 2}} in binary bisector notation
The real prohibition of Christmas prior to the 19th century = s(1801, 1900 {2 ` 2} 2 {1 ` 2} 1 {2} 1, 2) in strong array notation