The Lattice of Natural Numbers and The Sublattice of it. The Set of Prime Numbers.

Marek Chmur

Warsaw University, Bialystok

Summary.

Basic properties of the least common multiple and the greatest common divisor. The lattice of natural numbers (${\rm L}_{\Bbb N}$) and the lattice of natural numbers greater than zero (${\rm L}_{\Bbb N^+}$) are constructed. The notion of the sublattice of the lattice of natural numbers is given. Some facts about it are proved. The last part of the article deals with some properties of prime numbers and with the notions of the set of prime numbers and the $n$-th prime number. It is proved that the set of prime numbers is infinite.

MML Identifier: NAT_LAT

Contents (PDF format)

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