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Post by 《§》carbonara <3〖ƧƐ〗 on Jul 9, 2015 7:12:55 GMT
10&10 = {10,10,10,10,10,10,10,10,10,10} ("Decadecatrix") EDIT: it is about f ω8+9(10) in the fast-growing hiearchy! f ω10+10(10) ( ͡° ͜ʖ ͡°) Define it properly if it's your entry :V First, define Fast-Growing Hiearchy: f 0(n) = n+1 f a+1(n) = f a(f a(...(f a(n))...)) f a(n) = f a[n](n) iff "a" is a limit ordinal Then, define Wainer's Hiearchy: ω[n] = n ω2[n] = ω+n ωk[n] = w(k-1)+n ω 2[n] = ωn ω k[n] = ω k-1n ω ω[n] = 2ω[n] = ω nkω[n] = ( k-1ω )nε 0[n] = nω ( ωω = ω ωω...ω = ε 0) ε 1[n] = nε 0ε k[n] = k-1ε nζ 0[n] = ε εε...ε0ζ 1[n] = ε ...ε(ζ0+1) (ε_ε_ε_..._ε_(ζ 0+1)) EDIT: my entry is f ωω(10 100) >> {10 100,10 100,10 100,...,10 100,10 100,10 100,} with 10 100 entries (my "Rabb2tplex") |
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Post by P1kachu on Jul 9, 2015 8:07:01 GMT
My entry is fωω(10&10)
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Post by 《§》carbonara <3〖ƧƐ〗 on Jul 9, 2015 8:17:25 GMT
f ÏÏ2(40) is my entry ( ͡° ͜ʖ ͡°) |
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Post by P1kachu on Jul 9, 2015 8:20:25 GMT
f ÏÏ2(40) is my entry ( ͡° ÍÊ Í¡Â°) f_w^^5(100) ( ͡° ͜ʖ ͡°) MINE ( ͡° ͜ʖ ͡°) |
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Post by 《§》carbonara <3〖ƧƐ〗 on Jul 9, 2015 8:21:30 GMT
f ÏÏ2(40) is my entry ( ͡° ÍÊ Í¡Â°) f_w^^5(100) ( ͡° ÍÊ Í¡Â°) MINE ( ͡° ÍÊ Í¡Â°) f 100Ï(100) ( ͡° ͜ʖ ͡°) |
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Post by P1kachu on Jul 9, 2015 8:22:41 GMT
fÏÏÏÏÏ(100) ( ͡° ͜ʖ ͡°)
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Post by 《§》carbonara <3〖ƧƐ〗 on Jul 9, 2015 8:23:58 GMT
much smaller than my number :/ 100ω = ω^^100 = ω ωω... with 100 ω's... |
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Post by P1kachu on Jul 9, 2015 8:25:08 GMT
fÏÏ(100) ( ͡° ͜ʖ ͡°)
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Post by 《§》carbonara <3〖ƧƐ〗 on Jul 9, 2015 8:42:02 GMT
that's f e0(n) (with e the greek letter epsilon)! f e0(1000) |
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Post by P1kachu on Jul 9, 2015 9:29:19 GMT
fe1(1000)
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Post by 《§》carbonara <3〖ƧƐ〗 on Jul 9, 2015 11:03:27 GMT
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Post by Deleted on Jul 9, 2015 17:20:40 GMT
∞ - ∞ ( ͡° ͜ʖ ͡°) You should become a mathematician, you are very good with these types of things  |
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Post by 《§》carbonara <3〖ƧƐ〗 on Jul 9, 2015 19:09:09 GMT
∞ - ∞ ( ͡° ͜ʖ ͡°) You should become a mathematician, you are very good with these types of things ∞ isn't a well-defined number, so using it doesn't make any sense A definition could be: "Let f(S) be the number of elements of the set S. I create the set W such that 0 is in W and that for any number n, n+1 is also in the set. ∞ = f(W)" |
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Post by P1kachu on Jul 10, 2015 0:06:23 GMT
f eââe(100) Where â represents the up arrow notation, but downwards ( ͡° ͜ʖ ͡°) |
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Post by 《§》carbonara <3〖ƧƐ〗 on Jul 10, 2015 7:14:19 GMT
f e↓↓e(100) Where ↓ represents the up arrow notation, but downwards ( ͡° ͜ʖ ͡°) down-arrow notation exists, but it is a primitive recursive function, nothing to see with your function |
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