0 is natural

November 21, 2020

Apparently some people believe that 00 is not a natural number. Some people seem to argue that 00 is not even odd. One such person used to be my math teacher.

I think 00 is so obviously even it’s not even worth arguing, but there is reason to say that 00 isn’t natural. This is why I’ve compiled a number of reasons why 00 should be considered a natural number.

0N0 \in \mathbb{N}

  1. 00 is the most natural number: How many apples do you have right now?
  2. The most natural definition of odd naturals is nN:2n+1\forall n \in \mathbb{N}: 2n+1. If 00 isn’t natural, it would be 2n12n-1.
  3. A sum from 00 to nn has nn elements. A sum from 11 to nn has n1n - 1 elemnts.
  4. Pascal’s triangle starts from (00)0 \choose 0.
  5. The IB, the MIT and TUDelft say that 00 is natural.
  6. Units are 10010^0 (or in general b0b^0)
  7. Most programming languages and programmers start counting from 00 (Matlab and Julia are the exception)