Division, Zero free write

Zero:
- The symbol for 'nothing'
- Looks like a hole
- Under the map z -> 1/z is sent to the point infinity
- 0 times infinity = 0
- the additive identity in a ring
- obliterates everything under multiplication (even in an arbitrary ring)
- the 'center', versus infinity as 'the limit'
- 0! = 1, because there is only one way to arrange nothing
- nCk = 0 if k > n, because there is no way to select a set of k items from only n < k items

Division:
- Multiplicative inversion
- Given an arbitrary integral domain one can construct a fraction field where multiplication makes sense
- Makes sense in a division ring
- More problematic than multiplication because the integers have no multiplicative inverse in the integers
- Perhaps motivated the advent of rational numbers
- 'Division by 0' makes perfect sense in Riemann sphere