this post was submitted on 26 Dec 2024
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How about ANY FINITE SEQUENCE AT ALL?

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[–] SwordInStone@lemmy.world 77 points 2 days ago* (last edited 2 days ago) (7 children)

No, the fact that a number is infinite and non-repeating doesn't mean that and since in order to disprove something you need only one example here it is: 0.1101001000100001000001... this is a number that goes 1 and then x times 0 with x incrementing. It is infinite and non-repeating, yet doesn't contain a single 2.

[–] GreyEyedGhost@lemmy.ca 36 points 2 days ago (1 children)

This proves that an infinite, non-repeating number needn't contain any given finite numeric sequence, but it doesn't prove that an infinite, non-repeating number can't. This is not to say that Pi does contain all finite numeric sequences, just that this statement isn't sufficient to prove it can't.

[–] SwordInStone@lemmy.world 13 points 2 days ago

you are absolutely right.

it just proves that even if Pi contains all finite sequences it's not "since it oa infinite and non-repeating"

[–] bradorsomething@ttrpg.network 1 points 1 day ago (1 children)

1/3 is infinite in decimal form, as a more common example. 0.333333333….

[–] AccountMaker@slrpnk.net 13 points 2 days ago

That was quite an elegant proof

[–] lazynooblet@lazysoci.al 6 points 2 days ago

What about in the context of Pi?

[–] Thavron@lemmy.ca 3 points 2 days ago (2 children)

Doesn't the sequence "01" repeat? Or am I misunderstanding the term.

[–] Sconrad122@lemmy.world 7 points 2 days ago

A nonrepeating number does not mean that a sequence within that number never happens again, it means that the there is no point in the number where you can predict the numbers to follow by playing back a subset of the numbers before that point on repeat. So for 01 to be the "repeating pattern", the rest of the number at some point would have to be 010101010101010101... You can find the sequence "14" at digits 2 and 3, 104 and 105, 251 and 252, and 296 and 297 (I'm sure more places as well).

[–] SwordInStone@lemmy.world 2 points 2 days ago

yeah, but non-repeating in terms of decimal numbers usually mean: you cannot write it as 0.(abc), which would mean 0.abcabcabcabc...

[–] Azzu@lemm.ee 1 points 2 days ago (2 children)

But didn't you just give a counterexample with an infinite number? OP only said something about finite numbers.

[–] Strobelt@lemmy.world 19 points 2 days ago* (last edited 2 days ago) (1 children)

They were showing that another Infinite repeating sequence 0.1010010001... is infinite and non-repeating (like pi) but doesn't contain all finite numbers

[–] Azzu@lemm.ee 7 points 2 days ago (1 children)

You mean infinite and non- repeating?

[–] Strobelt@lemmy.world 2 points 2 days ago

This! Fixed it. Thanks!

[–] SwordInStone@lemmy.world 9 points 2 days ago

"2" is a finite sequence that doesn't exist in the example number

[–] underwire212@lemm.ee -2 points 2 days ago (1 children)

Wouldn’t binary β€˜10’ be 2, which it does contain? I feel like that’s cheating, since binary is just a mode of interpreting information …all numbers, regardless of base, can be represented in binary.

[–] Teepo@sh.itjust.works 12 points 2 days ago (2 children)

They're not writing in binary. They're defining a base 10 number that is 0.11, followed by a single 0, then 1, then two 0s, then 1, then three 0s, then 1, and so on. The definition ensures that it never repeats, but because it only contains 1 and 0, it would never contain any sequence with the numbers 2 through 9.

[–] weker01@sh.itjust.works 5 points 2 days ago

And you can strongman this by first using the string 23456789 at the start. It does contain all base 10 digits but not 22.

[–] SwordInStone@lemmy.world 2 points 2 days ago

Thanks for the consideration for my pronouns XD

he/him if it ever matters