To answer this question, we first need to define what “even” means. All even numbers can be expressed in the algebraic form 2n, where n is any whole number, positive, negative or zero (i.e. n is an integer). Thus 0 = 2 x 0, 2 = 2 x 1, 4 = 2 x 2, and so on. All odd numbers can be expressed in the form 2n + 1, thus 1 = (2 x 0) + 1, 3 = (2 x 1) + 1, 5 = (2 x 2) + 1, etc.
Zero cannot be odd, because there is no whole number n such that 2n + 1 = 0.
That means that 0 is even!
Can 0 also be an odd number? Again, we first need to define what “odd” means and the common definition is very similar to the definition of even. An odd number is a number n which can be written as n=2⋅ k+1 for some whole number k.
Can we write 0=2⋅k+1 for some whole number k? Nope. We can’t because solving this equation for k yields k=-1/2, which is not a whole number.
In fact, it is possible to have another thought: within the set composed of all the whole numbers, before an odd number we always find an even one. As zero comes before number one, which is an odd one, it means that zero has to be even.