Wikipedia:Reference desk/Archives/Mathematics/2024 February 21

= February 21 =

If zero would be even, then ...
I am commenting page https://en.wikipedia.org/wiki/Parity_of_zero

If zero would be even, then we would say the following.

1. snakes have zero legs, if zero would be even, we would say: snakes have an even number of legs.

2. pigs have zero wings, if zero would be even, we would say: pigs have an even number of wings.

Zero 0 objects divided in groups of b > 0 objects, will count 0 complete groups of b objects and 0 objects leftover, that means 0/b = (q, r) = (0, 0) for any b > 0.

Even integers are named even, because divided in groups of 2, will count at least one group of 2, but not less, having no leftover.

Considering "0 is even", suggesting that 0 will count at least one group of 2, that is false.

Generalization: 

For a >= 0 and b >= 0, where a/b = (q, r) => b * q + r = a a is incomplete aggregation, if q >= 0 and r > 0 a is complete aggregation, if q > 0 and r = 0 a = 0 is neutral aggregation, if q = 0 and r = 0 109.185.67.40 (talk) 10:31, 21 February 2024 (UTC)


 * 0 is 0 groups of two. "At least one" was a stipulation you tacked on without a justification. Remsense  诉  11:35, 21 February 2024 (UTC)
 * So you would say pigs have an uneven number of wings? ;) Anyway, try a forum such as Reddit for this, they allow debate. HansVonStuttgart (talk) 12:46, 21 February 2024 (UTC)
 * The way natural language is used in informal discourse may differ from mathematical discourse, where precise definitions matter. In everyday discourse, the statement that all mountains on Barbuda have one or several excellent ski resorts will be considered false or nonsensical. Translated into a formal logic statement, it becomes a (vacuously) true statement – Barbuda's highest elevation is 44.5 m. The mathematical definition of "even" leaves no room for doubt that $$0$$ is even, since $$\exists k\in\Z~(0=2k).$$ --Lambiam 13:55, 21 February 2024 (UTC)
 * (Almost) any statement about members of an empty set is true e.g. "All female US presidents have won a Nobel prize, walked on the moon, and held the world record for yodeling." :) cm&#610;&#671;ee&#9094;&#964;a&#671;&#954; 16:32, 21 February 2024 (UTC)
 * How is yodeling measured? —Tamfang (talk) —Tamfang (talk) 17:22, 22 February 2024 (UTC)
 * When I was first introduced to vacuous truths, I found it a lot easier to accept their truth by framing them negatively: if they were false, you should be able to find a counterexample. For obvious reasons, you can't. In this particular case: you cannot find a mountain on Barbuda without excellent ski resorts. :)
 * And now I see Timothy Gowers said the same thing. :) Double sharp (talk) 09:21, 24 February 2024 (UTC)
 * Would you cosider -2 as an even number? If so you have a rather strange gap in that every integer multiple of 2 except by 0 is an even number. One can do that of course but it doesn't correspond wit what mathematicians call an even number. NadVolum (talk) 18:02, 21 February 2024 (UTC)
 * Based off of "at least one" I would guess that all negative even numbers don't count either, which is weird (or I guess you could say, even weirder.) GalacticShoe (talk) 18:05, 21 February 2024 (UTC)
 * If all even numbers are at least 1, it follows (ex falso quodlibet&thinsp;) that all negative even numbers are odd. --Lambiam 18:35, 21 February 2024 (UTC)
 * Indeed, many people find negative numbers to be odd. GalacticShoe (talk) 18:48, 21 February 2024 (UTC)
 * Perhaps they're imaginary?😁 NadVolum (talk) 20:19, 21 February 2024 (UTC)
 * Sounds like a complex issue... GalacticShoe (talk) 02:00, 22 February 2024 (UTC)
 * I LOVE this community CiaPan (talk) 07:49, 23 February 2024 (UTC)
 * I LOVE this community CiaPan (talk) 07:49, 23 February 2024 (UTC)