In combinatorial number theory, the Lambek–Moser theorem splits the natural numbers into two complementary sets using any non-decreasing function and its inverse. It extends Rayleigh's theorem, which splits the natural numbers into complementary sets in a more restricted way by rounding the multiples of two irrational numbers. When a formula is known for the th natural number in a set, the Lambek–Moser theorem can be used to derive a formula for the th number not in the set.
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