Journal of Formalized Mathematics
Volume 3, 1991
University of Bialystok
Copyright (c) 1991 Association of Mizar Users

## 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

The terminology and notation used in this paper have been introduced in the following articles [10] [6] [12] [11] [1] [9] [2] [14] [4] [3] [7] [13] [5] [8]

Contents (PDF format)

#### Bibliography

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