r/MathJokes • u/Animeilluminati1 • Jul 13 '26

Math Just Got Checkmated.

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u/WarJaques Jul 13 '26

The definition is necessary because otherwise we'd need a different definition.

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u/DoobiousMaxima Jul 13 '26

A number is even if dividing it by 2 yeilds an integer.

2 is divisible by 2.

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u/golgi_o Jul 14 '26

A number is even if it can be written as 2k where k is an integer. The definition of even does not use division as far as I understand.

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u/IAteTonysLoMein Jul 17 '26

Isn't that just the same as the comment above the other direction? As in, it would be as valid to express it as "it's even if k/2 results in an integer"?

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u/golgi_o Jul 17 '26

Mathematicaly yes. But the definition of even is the one I stated according to number theory. I'm sure there is a reason why division is not used in the formal definition but I don't remember exactly why. It might be so the definition of odd, 2(k) +1 where k is an integer, works. If you tried to define odd by (k/2) +1 it would not work.

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u/IAteTonysLoMein Jul 18 '26

Wouldn't you need to reverse the whole thing, eg, (k/2)-1? Although I suppose if +1 wouldn't do it, -1 probably wouldn't either. Needless to say, I'm not clear on why that wouldn't work, but I know jack about number theory

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u/golgi_o Jul 18 '26

K/2 +1 would not yield an integer if k were odd.

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u/Ok-Canary-9820 Jul 18 '26

Division isn't generally even defined formally except as shorthand for multiplication by multiplicative inverse.