How to convince people that 0 is even

Question

Some people say that 0 is neither even nor odd. I say that 0 is even.

Is there a simple way to convince people that 0 is even and the statement that "0 is neither even nor odd" is false.

Answer 1

An integer, $x$, is defined to be even whenever it can be written in the form $x=2k$ where $k$ is some integer.

Examples: $6=2\cdot 3,~~ 10 = 2\cdot 5,~~ 2218 = 2\cdot 1109,~~ -4 = 2\cdot (-2)$

An integer, $x$, is defined to be odd whenever it can be written in the form $x=2k+1$ where $k$ is some integer.

Examples: $-3 = 2\cdot (-2) + 1,~~~ 9 = 2\cdot 4 + 1,~~~ 1001 = 2\cdot 500 + 1$

Remember that $0$ is itself an integer, and that $0 = 2\cdot \color{red}{0}$, which is in the form $0=2k$ with $k = \color{red}{0}$, therefore $0$ is even.