What’s special about ZERO?

(or: Much ado about Nothing)

Zero doesn’t actually exist. Think about it: by definition it isn’t anything, it’s nothing!! Even so, here are 5 facts every mathematician should know about Zero:

  1. Zero is the essential place-holder that makes place-value work (without Zero 15, 105 and 150 would all look the same).
  2. It is the only number you cannot divide by. Try it: your calculator will get cross and bothered.
  3. It has its own index law: $x^0=1$ (always true – it doesn’t matter what $x$ is)*
  4. It is the only number on the number line that is neither positive nor negative.
  5. You cannot write zero in Roman Numerals. I have a feeling this could be why there are no famous ancient Roman mathematicians.

*The only exception to rule 2 is of course – you’ve guessed it – when $x$ is zero ($0^0$ is undefined).