📂Number Theory

Definition of Even Numbers

Definition

Simple Definition

A number is said to be even if it has a remainder of $0$ when divided by $2$.

Complex Definition

$$a = 2 \cdot k$$ For any integer $a$, if there exists an integer $k$ that satisfies the above, then $a$ is considered Even. Integers that are not even are called Odd.

Explanation

There’s a question that reignites internet forums every cooldown period.

“Is $0$ even?”

The reason this sparks debate despite being taught in elementary school nationwide is simple. Many who are estranged from mathematics think with the premise of the ‘Simple Definition’ and that ‘$0$ cannot be divided’. Thus, fun banter ensues like “$0$ is a special number that is neither even nor odd” or “It’s a problem even Harvard hasn’t solved yet.” If you search ‘0 even’ on Google images, you can feel dizzy.

According to the Complex Definition, such questions are neatly terminated. The integer $0$ satisfies $$0 = 2 \cdot k$$ for $k=0$, making it unequivocally even. Not just that, but negative numbers like $-2$ and $-22$ are also even.