# 0 is natural

November 21, 2020

Apparently some people believe that $0$ is not a natural number. Some people seem to argue that $0$ is not even odd. One such person used to be my math teacher.

I think $0$ is so obviously even it’s not even worth arguing, but there is reason to say that $0$ isn’t natural. This is why I’ve compiled a number of reasons why $0$ should be considered a natural number.

# $0 \in \mathbb{N}$

- $0$ is the most natural number: How many apples do you have right now?
- The most natural definition of odd naturals is $\forall n \in \mathbb{N}: 2n+1$. If $0$ isn’t natural, it would be $2n-1$.
- A sum from $0$ to $n$ has $n$ elements. A sum from $1$ to $n$ has $n - 1$ elemnts.
- Pascal’s triangle starts from $0 \choose 0$.
- The IB, the MIT and TUDelft say that $0$ is natural.
- Units are $10^0$ (or in general $b^0$)
- Most programming languages and programmers start counting from $0$ (Matlab and Julia are the exception)