ok so everyone here is wrong. sit down and let me tell you what a number is.
numbers as you know it are mathematical objects. however, mathematicians have a more formalized view of what a (natural) number is. in fact there are many formalizations, but cardinal and ordinal numbers are the two most popular ones.
ordinal numbers are pretty straightforward.
basically the empty set: {} is defined to be 'zero'
then the next number after 0 -- the successor, as it's called in math, is simply the set containing 0: {0} or {{}}, or you can denote it as 1
then the next number is {0, 1} which is {{},{{}}}
and so on
then there are cardinal numbers. the idea of cardinal numbers is that you can group sets if they are of equal size. for example, the set {a,b} belongs to the same group as {c,d} because they have the same size. we can see they have the same size because we can pair up a with c and b with d. note that this size comparison procedure does not require any notion of numbers to define at all!
then, the smallest set of groups, basically the group containing just {}, is called 0. The next smallest group is called 1. et cetera.
