Is zero odd or even?

Some books say that even numbers start from 2 but if you consider the number line concept, I think zero(0) should be even because it is in between 1 and +1 (i.e in between two odd numbers). What is the real answer?

Answer

For that, we can try all the axioms formulated for even numbers. I’ll use only four in this case.

Note: In this question, for the sake of my laziness, I will often use Ne for even, and No for odd.

Test 1:

An even number is always divisible by 2.

We know that if x,yZ
and xyZ, then y is a divisor of x (formally y|x).

Yes, both 0,2Z and yes, 02 is 0 which is an integer. Passed this one with flying colors!


Test 2:

Ne+Ne results in Ne


Let’s try an even number here, say 2. If the answer results in an even number, then 0 will pass this test.     2Ne+0=2Ne   , so zero has passed this one!


Test 3:

Ne+No results in No

0+1No=1No

Passed this test too!


Test 4:

If n is an integer of parity P, then n2 will also be an integer of parity P.

We know that 2 is even, so 22 or 0 is also even.

Attribution
Source : Link , Question Author : mvar2011 , Answer Author : JSQuareD

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