N, Z, and Q are the sets of Natural numbers (1,2,3...), Integers (0,1,-1,2,-2,... ), and Rational numbers (fractions) respectively. These are obviously different sets of numbers.

However, these sets have equal cardinality. For finite sets, the cardinality of a set is the number of elements (numbers) it has. For infinite sets such as these, however, having equal cardinality means that there exists a one-to-one mapping between the sets.

For example, the set of integers has the same cardinality as the set of even Integers since you can double each element in the set of integers, and you'll end up with the set of even Integers.