 We saw above, in our discussion of complete divisibility, the problem with such reasoning applied to continuous lines: any line segment has the same number of points, so nothing can be inferred from the number of points in this way—certainly not that half the points (here, instants) means half the length (or time). The paradox fails as stated. But doesn’t the very claim that the intervals contain the same number of instants conflict with the step of the argument that concludes that there are half as many \(A\)-instants as \(C\)-instants? This issue is subtle for infinite sets: to give a different example, 1, 2, 3, … is in 1:1 correspondence with 2, 4, 6, …, and so there are the same number of each. It is in this sense of 1:1 correspondence—the precise sense of ‘same number’ used in mathematics—that any finite line has the same number of points as any other. However, informally speaking, there are also ‘half as many’ even numbers as whole numbers: the pairs (1, 2), (3, 4), (5, 6), … can also be put into 1:1 correspondence with 2, 4, 6, …. Similarly, there are—informally speaking—half as many \(A\)-instants as \(C\)-instants: \(A\)-instants are in 1:1 correspondence with pairs of \(C\)-instants. So there is no contradiction in the number of points: the informal half equals the strict whole (a different solution is required for an atomic theory, along the lines presented in the final paragraph of this section). 