198
submitted 1 day ago* (last edited 1 day ago) by Melatonin@lemmy.dbzer0.com to c/asklemmy@lemmy.ml

How about ANY FINITE SEQUENCE AT ALL?

you are viewing a single comment's thread
view the rest of the comments
[-] SwordInStone@lemmy.world 68 points 23 hours ago* (last edited 19 hours ago)

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 26 points 17 hours ago

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 8 points 12 hours 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"

[-] AccountMaker@slrpnk.net 12 points 21 hours ago

That was quite an elegant proof

[-] lazynooblet@lazysoci.al 6 points 22 hours ago

What about in the context of Pi?

[-] Thavron@lemmy.ca 3 points 20 hours ago

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

[-] Sconrad122@lemmy.world 6 points 19 hours 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 1 points 19 hours ago

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

[-] underwire212@lemm.ee -1 points 13 hours ago

Wouldn’t binary ‘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 9 points 13 hours ago

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 13 hours 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 3 points 12 hours ago

Thanks for the consideration for my pronouns XD

he/him if it ever matters

[-] Azzu@lemm.ee 1 points 22 hours ago

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

[-] Strobelt@lemmy.world 17 points 22 hours ago* (last edited 13 hours ago)

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 5 points 19 hours ago

You mean infinite and non- repeating?

[-] Strobelt@lemmy.world 1 points 13 hours ago

This! Fixed it. Thanks!

[-] SwordInStone@lemmy.world 9 points 21 hours ago

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

this post was submitted on 26 Dec 2024
198 points (98.5% liked)

Asklemmy

44173 readers
1926 users here now

A loosely moderated place to ask open-ended questions

Search asklemmy 🔍

If your post meets the following criteria, it's welcome here!

  1. Open-ended question
  2. Not offensive: at this point, we do not have the bandwidth to moderate overtly political discussions. Assume best intent and be excellent to each other.
  3. Not regarding using or support for Lemmy: context, see the list of support communities and tools for finding communities below
  4. Not ad nauseam inducing: please make sure it is a question that would be new to most members
  5. An actual topic of discussion

Looking for support?

Looking for a community?

~Icon~ ~by~ ~@Double_A@discuss.tchncs.de~

founded 5 years ago
MODERATORS