this post was submitted on 21 Jun 2025
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Math Memes

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[–] fargeol@lemmy.world 57 points 1 month ago (4 children)

Theorem - All numbers are interesting

Demonstration:

  • 0 is interesting
  • if n is interesting, n+1 is either interesting or not interesting.
    -- If n+1 is not interesting, we take interest in it as it it the smallest non-interesting number.
  • Therefore, n+1 is interesting

By induction, all numbers are interesting

[–] CompassRed@discuss.tchncs.de 6 points 1 month ago* (last edited 1 month ago)

My favorite version of this proof:

Let S be the subset of natural numbers that are not interesting. Suppose by way of contradiction that S is inhabited. Then by the well ordering principle of natural numbers, there is a least such element, s in S. In virtue of being the least non interesting number, s is in fact interesting. Hence s is not in S. Since s is in S and not in S, we have derived a contradiction. Therefore our assumption that S is inhabited must be false. Thus S is empty and there are no non interesting numbers.

Counterproof:

n+1 is not the smallest non-interesting number... n-1 is.

[–] match@pawb.social 2 points 1 month ago (1 children)

What about 31? That's the smallest non-interesting number so if we take that as the first n, then every n+1 is either interesting or the second-smallest non-interesting number, and the second smallest non-interesting number is still not interesting.

[–] Stillwater@sh.itjust.works 10 points 1 month ago

31 is prime, that's interesting isn't it?

what about the real, non-rational numbers?

[–] magic_lobster_party@fedia.io 14 points 1 month ago (1 children)

I think 6 is a rather big number. It’s more than I can count on one hand.

[–] KickMeElmo@sopuli.xyz 13 points 1 month ago (1 children)

Start counting in binary. Gets you to 31 on one hand, 1023 on two.

[–] Carvex@lemmy.world 5 points 1 month ago

Chernobyl math

[–] elevenbones@sh.itjust.works 11 points 1 month ago

I've seen smaller 😏

[–] 5714@lemmy.dbzer0.com 9 points 1 month ago (2 children)

I don't think you can induce all numbers from n+1

True, You can only induce natural numbers from this.

However, you could extend it to the positive reals by saying [0,1) is a small number. And building induction on all of those.

You could cover negative and even complex numbers if “small” is a reference to magnitude of a vector, but that is a slippery slope…

In a very not rigorous way, you can cover combinations of ordinal numbers and even non-numbers if you treat them as orthogonal “unit vectors” and the composite “number” as a vector in an infinite vector space which again allows you to specify smallness as a reference to magnitude like we did for the complex numbers.

If you multiply two not really numbers, just count the product as a new dimension for the vector. Same with exponentiation. Same with non math shit like a cow or the color orange. Count all unique things as a unique dimension to a vector then by our little vector magnitude hack, everything is a small number, even things that aren’t numbers. QED.


This proof is a joke, broken in many ways, but the most interesting is the question of if you can actually have a vector with an uncountably infinite (or higher ordinals) of dimensions and what the hell that even means.

[–] BodilessGaze@sh.itjust.works 5 points 1 month ago* (last edited 1 month ago) (2 children)

Sure you can. Proof:

0 is a number.

If n is a number, n+1 is also a number.

Therefore, by mathematical induction, we can induce all numbers.

[–] BlackRoseAmongThorns@slrpnk.net 5 points 1 month ago

☝🏽🤓 The naturals are hardly all numbers, considering they're only a countably infinite subset of the reals.

[–] 5714@lemmy.dbzer0.com 1 points 1 month ago

Weird. There are no numbers that can't be added. I wanted that.

[–] Evil_Shrubbery@lemm.ee 8 points 1 month ago

But what abut 10⁸⁰ + 1 ??

[–] Ludrol@szmer.info 3 points 1 month ago

This is a poor definition, a small number is usually defined by an inequality.

[–] hypeerror@sh.itjust.works 2 points 1 month ago
[–] unhrpetby@sh.itjust.works 2 points 1 month ago

Different variation of the Sorites Paradox.