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submitted 1 month ago by Kierunkowy74@fedit.pl to c/mathmemes
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[-] 5714@lemmy.dbzer0.com 9 points 1 month ago

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

[-] AnarchoEngineer@lemmy.dbzer0.com 9 points 1 month ago

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)

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.

this post was submitted on 21 Jun 2025
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Math Memes

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Memes related to mathematics.

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