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?
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.
An even number is always divisible by 2.
We know that if x,y∈Z
and xy∈Z, then y is a divisor of x (formally y|x).
Yes, both 0,2∈Z and yes, 02 is 0 which is an integer. Passed this one with flying colors!
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. 2⏟Ne+0=2⏟Ne , so zero has passed this one!
Ne+No results in No
Passed this test too!
If n is an integer of parity P, then n−2 will also be an integer of parity P.
We know that 2 is even, so 2−2 or 0 is also even.