About: Lambek–Moser theorem

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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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rdfs:label	Lambek–Moser theorem (en)
rdfs:comment	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. (en)
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dcterms:subject	Theorems in number theory Integer sequences
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Link from a Wikipage to another Wikipage	Prime-counting function Monotonic function Beatty sequence Bounded function Algorithm Theorems in number theory Complement (set theory) Galois connection Composite number Leo Moser Parity (mathematics) Irrational number Proof without words Integer sequences D. H. Lehmer Edsger W. Dijkstra Even number Histogram Inverse function Prime number Joachim Lambek Hofstadter sequence The American Mathematical Monthly Bulletin of the AMS Square (algebra) Square root Integer Natural number Odd number Samuel Beatty (mathematician) Viggo Brun Combinatorial number theory Odious number Evil number Pronic number Thue–Morse sequence Primitive Pythagorean triple Binary representation
Link from a Wikipage to an external page	https://www.math.ust.hk/excalibur/v3_n4.pdf https://www.cs.utexas.edu/users/EWD/ewd07xx/EWD753.PDF https://www.cs.utexas.edu/users/EWD/transcriptions/EWD07xx/EWD776.html https://www.emis.de/journals/INTEGERS/papers/o9/o9.Abstract.html https://books.google.com/books%3Fid=DvX90EKMxGwC&pg=PA11 https://books.google.com/books%3Fid=EGQSAAAAIAAJ&pg=PA123 https://books.google.com/books%3Fid=ZXGYDwAAQBAJ&pg=PA32 https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/generating-nonpowers-by-formula https://projecteuclid.org/euclid.pjm/1103044611
sameAs	Lambek–Moser theorem Lambek–Moser theorem Lambek–Moser theorem
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has abstract	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. There are two parts to the Lambek–Moser theorem. One part states that two functions that are inverse, in a certain sense, can be used to split the natural numbers into two complementary subsets, and the other part states that every complementary partition can be constructed in this way. As well as the Beatty sequences of Rayleigh's theorem, other pairs of complementary sets of natural numbers to which the Lambek–Moser theorem can be applied include the even numbers and the odd numbers, the evil numbers and the odious numbers, the prime numbers and the non-primes (1 and the composite numbers), and the th powers and non-powers. The Lambek–Moser theorem is named for Joachim Lambek and Leo Moser, who published it in 1954, and should be distinguished from an unrelated theorem of Lambek and Moser, later strengthened by Wild, on the number of primitive Pythagorean triples. (en)
gold:hypernym	Generalization
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is Link from a Wikipage to another Wikipage of	Beatty sequence Deaths in June 2014 Complementary sequences Leo Moser Joachim Lambek Hofstadter sequence List of theorems Lambek (disambiguation) Polite number Lambek-Moser theorem
is Wikipage redirect of	Lambek-Moser theorem

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