Not in terms of cardinality, at least. Consider the set of natural numbers {0, 1, 2, ...}. This set is clearly of infinite size. If we remove 0, then we have a

Not in terms of cardinality, at least. Consider the set of natural numbers {0, 1, 2, ...}. This set is clearly of infinite size. If we remove 0, then we have a set {1, 2, ...} with, in principle, one less element than we started with -- yet it is also clearly infinite. However, these sets have exactly the same number of elements (i.e. "infinity-1 is the same size as infinity") -- I can pair 0 with 1, 1 with 2, 2 with 3, and so on, so that every number in the first set is uniquely paired with a number in the second set, and vice versa. Arithmetically, I can write `f(x) = x + 1` to go from the first set to the second set, and `g(x) = x - 1` to go from the second set back to the first set, and "clearly" we don't lose any information performing `f` followed by `g` -- no two elements land in the same place in either direction.