New Largest Number in Snap*!*

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1

BMS has been officially implemented in Snap*!*.

I’ve taken an over 1-year long hiatus for so far now. Back then, the largest number I ever made back then was only a mere φ(ω,0). But now, I have arrived back again to make my official comeback. I said I would make ψ(Ω_2), and even ψ(Ω_ω). However, this new program I made is an official interpretation of the legendary Bashicu Matrix System, which reaches far past all of these, obliterating all that was known before, making an incomprehensible jump from φ(ω,0), which is (0,0)(1,1)(2,1)(3,0) in this notation. The limit is (0,0,0,0,…)(1,1,1,1,…) with as much 0s as there are 1s. This is what I could consider my magnum opus for now. I don’t know how to make it sound much more intense, but it is just so grand that I was able to do this, I went from a starting point, and jumped straight to the very end. And what’s even more astonishing is that I was able to make it in just 1 hour, based off of a python script I made prior. For now, here is what lies the ultimately largest number officially created in Snap*!*, for now.

You can test some example ordinals here (make sure to input an index after inputting each of these matrices):

(0)(1) - ω

(0)(1)(1) - ω^2

(0)(1)(2) - ω^ω

(0,0)(1,1) - ε0

(0,0)(1,1)(1,1) - ε1

(0,0)(1,1)(2,0) - εω

(0,0)(1,1)(2,0)(3,1) - εε0

(0,0)(1,1)(2,1) - ζ0

(0,0)(1,1)(2,1)(2,1) - η0

(0,0)(1,1)(2,1)(3,0) - φ(ω,0)

(0,0)(1,1)(2,1)(3,1) - Γ0

(0,0)(1,1)(2,1)(3,1)(4,0)(3,0) - ψ(Ω^(Ω^ω*ω))

(0,0)(1,1)(2,2) - ψ(Ω_2)

(0,0,0)(1,1,1) - ψ(Ω_ω) (Extended Buchholz’s OCF)

(0,0,0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)(2,2,1) - ψ(Ω_ω*(Ω+1))

(0,0,0)(1,1,1)(2,1,0)(1,1,1) - ψ((Ω_ω)^2)

(0,0,0)(1,1,1)(2,1,0)(3,2,0) - ψ(Ω_(ω+1))

(0,0,0)(1,1,1)(2,1,1) - ψ(Ω_(ω^2))

(0,0,0)(1,1,1)(2,1,1)(3,1,0) - ψ(Ω_Ω)

(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0) - ψ(Ι) (Multivariable Buchholz’s OCF)

(0,0,0)(1,1,1)(2,1,1)(3,1,1) - ψ(Ι_ω)

(0,0,0)(1,1,1)(2,2,0) - ψ(Ω_(Τ+1)) (2-shifted OCF)

(0,0,0)(1,1,1)(2,2,1) - ψ(Τ_ω)

(0,0,0)(1,1,1)(2,2,1)(3,0,0) - ψ(C(1{ω}0)) (Small Dropping Ordinal)

(0,0,0)(1,1,1)(2,2,2) - (α:α(ω^-)) (Stability)

(0,0,0,0)(1,1,1,1) - ψ(L[ω]) - (LOCF)

(0,0,0,0,0)(1,1,1,1,1) - ???

Limit - {(0)(1), (0,0)(1,1), (0,0,0)(1,1,1), (0,0,0,0)(1,1,1,1), …} = PTO(Z2)

Here it is. The largest number ever devised in Snap*!* as of 8/4/26:

Have fun with the program! Let me know what you all think of this.

2

You should probably change the title to something more descriptive like:

It is complete: BMS in Snap!

Anyways sick project!

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BMS blocks
BMS blocks435×102 42.8 KB
Script picture of all the blocks used in this program. Each of them represent an action in BMS.

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I’m bad at math lol (So idk how to use it)

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You can use one of the example matrices above, copy paste them into the text box, then it will ask you to input a number, such as 3 or 4 (too large numbers can make it take forever). For example, inputting (0,0,0)(1,1,1)(2,2,0) first, then inputting 3 after it asked you, will make it generate (0,0,0)(1,1,1)(2,2,0)[3], or (0,0,0)(1,1,1)(2,1,1)(3,1,1)(4,1,1).

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Same, is it possible to do the BMS limit?

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Not the BMS limit itself, but you can do some elements of the fundamental sequence of the limit of BMS by inputting (0,0,0,0,…)(1,1,1,1,…) into it, where there are as many 0s as 1s, and the amount of 0s and 1s are what index of the limit sequence it is. For example, lim(BMS)[3] = (0,0,0)(1,1,1) = ψ(Ω_ω)