 Craig’s point is this. Two sets \(A\) and \(B\) are the same size just in case they can be put into one-to-one correspondence, that is, if and only if every member of \(A\) can be correlated with exactly one member of \(B\) in such a way that no member of \(B\) is left out. In the case of infinite sets, this notion of “same size” yields results like the following: the set of all natural numbers (let this be \(A\)) is the same size as the set of squares of natural numbers (\(B\)), since every member of \(A\) can be correlated with exactly one member of \(B\) in a way that leaves out no member of \(B\) (correlate \(0\leftrightarrow 0\), \(1\leftrightarrow1\), \(2\leftrightarrow4\), \(3\leftrightarrow9\), \(4\leftrightarrow 16\),…). This is a case—recognized in fact as early as Galileo (Dialogues Concerning Two New Sciences)—where two infinite sets have the same size but, intuitively, one of them, as a proper subset, appears to be smaller than the other.