snarkophilus has a good answer, I just want to add that it depends on how you define "bigger." If you use a strict superset/subset relation, e.g., every integer is also a rational, but some rationals are not integers, then by this relation you could claim that the set of rationals is "bigger" than the set of integers. But the answer given by snarkophilus (and some other earlier comments) uses a definition by which two sets are considered to be of equal size if there is a one-to-one mapping between them. A perhaps counter-intuitive result is that an infinite set can often be mapped one-to-one to a proper subset of itself. An even simpler example than the real vs. complex or integers vs. rational would be the set of integers versus the set of even integers. Clearly the set of even integers is a proper subset of the set of integers, so by the definition towards which you seem inclined, the set of integers would indeed be "bigger." But there exists a one-to-one mapping, map each integer to its double, and this is a one-to-one mapping between the set of integers and the set of even integers. For each integer, there is a corresponding even integer, and for each even integer, there is a corresponding integer. So using cardinality to determine which set is "bigger," we would conclude that these two sets are of the same size, even though one clearly includes everything the other includes and more.