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Keep the largest number round 2 Jul 11, 2015 0:03:35 GMT

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Post by P1kachu on Jul 11, 2015 0:03:35 GMT

Jul 10, 2015 7:14:19 GMT 《§》carbonara <3〖ƧƐ〗 said:

Jul 10, 2015 0:06:23 GMT P1kachu said:

f_eââe(100)

Where â represents the up arrow notation, but downwards ( Í¡Â° ÍÊ Í¡Â°)

down-arrow notation exists, but it is a primitive recursive function, nothing to see with your function

It's by my own definition ( ͡° ͜ʖ ͡°)

My name should have been Tetramethyldiaminobenzhydrylphosphinous Acid, but it only accepts 30 and below letters

《§》carbonara <3〖ƧƐ〗
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Keep the largest number round 2 Jul 11, 2015 7:20:40 GMT via mobile

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Post by 《§》carbonara <3〖ƧƐ〗 on Jul 11, 2015 7:20:40 GMT

Jul 11, 2015 0:03:35 GMT P1kachu said:

Jul 10, 2015 7:14:19 GMT 《§》carbonara <3〖ƧƐ〗 said:

down-arrow notation exists, but it is a primitive recursive function, nothing to see with your function

It's by my own definition ( ͡° ͜ʖ ͡°)

you can't define a notation which conflict with another.

P1kachu
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Keep the largest number round 2 Jul 11, 2015 9:53:45 GMT

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Post by P1kachu on Jul 11, 2015 9:53:45 GMT

Jul 11, 2015 7:20:40 GMT 《§》carbonara <3〖ƧƐ〗 said:

Jul 11, 2015 0:03:35 GMT P1kachu said:

It's by my own definition ( Í¡Â° ÍÊ Í¡Â°)

you can't define a notation which conflict with another.

Let D_n(k) = k_{k_{k_{k_{k_k...}}}} Where there are n k's ( ͡° ͜ʖ ͡°)

My name should have been Tetramethyldiaminobenzhydrylphosphinous Acid, but it only accepts 30 and below letters

《§》carbonara <3〖ƧƐ〗
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Keep the largest number round 2 Jul 11, 2015 11:05:18 GMT

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Post by 《§》carbonara <3〖ƧƐ〗 on Jul 11, 2015 11:05:18 GMT

Jul 11, 2015 9:53:45 GMT P1kachu said:

Jul 11, 2015 7:20:40 GMT 《§》carbonara <3〖ƧƐ〗 said:

you can't define a notation which conflict with another.

Let D_n(k) = k_{k_{k_{k_{k_k...}}}} Where there are n k's ( ͡° ͜ʖ ͡°)

what is the final subscript? 0?

My turn:

φ(0,0) = ω, φ(0,β) = ω^β
φ(1,0) = ω^{ω^{^...}} = ε₀, φ(1,β) = ε_β
φ(2,0) = ε_{ε_{ε_{..._ε₀}}} = ζ₀, φ(2,β) = ζ_β
φ(3,0) = ζ_{ζ_{ζ_{..._ζ₀}}} = η₀, φ(3,β) = η_β

Formal definition: φ(α,β) is the (β+1)th fixed point of φ(α-1,0) if α is a successor, otherwise the limit of φ(α,φ(α,φ(...(φ(α,0))...))

φ(φ(φ(...(φ(0,0)...),0),0) = Γ₀ (the first fixed point of this function: Γ₀ = φ(Γ₀,0))

This is the Veblen's hiearchy.

My entry is: f_φ(69,69)(10¹⁰⁰) ( ͡° ͜ʖ ͡°)

Last Edit: Jul 11, 2015 11:10:56 GMT by 《§》carbonara <3〖ƧƐ〗

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Keep the largest number round 2 Jul 12, 2015 0:04:13 GMT

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Post by P1kachu on Jul 12, 2015 0:04:13 GMT

f_Ï(69,69)(f_Ï(69,69)(f_Ï(69,69)(10¹⁰⁰))) ( ͡° ͜ʖ ͡°)

My name should have been Tetramethyldiaminobenzhydrylphosphinous Acid, but it only accepts 30 and below letters

《§》carbonara <3〖ƧƐ〗 Owner Maths Lover <3 <3 <3 10000000000000000000 times stronger than pure sulfuric acid ( ͡° ͜ʖ ͡°) Posts: 912 Favorite Acid: Trifluoromethanesulfonic Acid Favorite Scientist: P1kachu Favorite Admin: Miguel888	Keep the largest number round 2 Jul 15, 2015 15:16:49 GMT via mobile Quote Select Post Deselect Post Link to Post Member Give Gift Back to Top Post by 《§》carbonara <3〖ƧƐ〗 on Jul 15, 2015 15:16:49 GMT Jul 12, 2015 0:04:13 GMT P1kachu said: f_φ(69,69)(f_φ(69,69)(f_φ(69,69)(10¹⁰⁰))) ( ͡° ͜ʖ ͡°) Read again, FGH has missing parameters xP

10^1 Guest	Keep the largest number round 2 Mar 14, 2021 6:35:03 GMT Quote Select Post Deselect Post Link to Post Back to Top Post by 10^1 on Mar 14, 2021 6:35:03 GMT 10^1

10^100 Guest	Keep the largest number round 2 Mar 14, 2021 6:35:45 GMT Quote Select Post Deselect Post Link to Post Back to Top Post by 10^100 on Mar 14, 2021 6:35:45 GMT 10^100

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Keep the largest number round 2

Post by P1kachu on Jul 11, 2015 0:03:35 GMT

Post by 《§》carbonara <3〖ƧƐ〗 on Jul 11, 2015 7:20:40 GMT

Post by P1kachu on Jul 11, 2015 9:53:45 GMT

Post by 《§》carbonara <3〖ƧƐ〗 on Jul 11, 2015 11:05:18 GMT

Post by P1kachu on Jul 12, 2015 0:04:13 GMT

Post by 《§》carbonara <3〖ƧƐ〗 on Jul 15, 2015 15:16:49 GMT

Post by 10^1 on Mar 14, 2021 6:35:03 GMT

Post by 10^100 on Mar 14, 2021 6:35:45 GMT

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