>>11519299I'm not sure if it matters. If you can associate each item of the two sets, they are the same size, in terms of cardinality, I think. That is true even if one is a subset of the other. I'm not sure why zero should be an issue here.
>> 11517536> Zero is neither even nor odd. No matter how infinity you count, you will always be short one even. There is an odd number of numbers, even in infinity.You only need a one-to-one mapping. Map zero to whatever element you like and then shift the sequences of odd and even numbers to make room for zero. If you have such a one-to-one mapping, you know they are of the same "size of infinity".
Take the set {-1,0,1,2,...} := S and N. Map S + 1 to N. That should be a one-to-one mapping, no?
Even though you "have an extra element" (which actually makes no sense when you talk about infinity) you still can find such a bijection, which is also why the rational and natural numbers are of the same size of infinity, no?
