Who has more elements, all integers or natural numbers? or the same?

Please include a reason. The fact that 0 is the set of integers and not all natural numbers is not the answer according to my teacher. Furthermore, saying they are equal, because the Cardinal both are infinite, not is acceptable. This is not an easy question, I suppose.

Caution: people use different "whole" to mean different things. For me, "integer" means "real lack fractional part number" – ie, as a whole. So for me, -1, -2, etc., are integers. However, others define Natural numbers as or sometimes more. You must be explicit. But it makes no difference to the answer here (for details of why), because in all cases, you can put all the numbers in a set by a combination of 1-1 with another series – which means that the same size. [The only detail here is written specific associations between the two groups, depending on what you mean by "whole".] In fact, the number of functions rational of the form X / Y (and not equal to 0) is exactly as big as all the natural numbers for the same reason.

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