Integers, ℤ

Abstract

In the article the following concepts were introduced: the set of integers ( ) and its elements (integers), congruences (i1 ≡ i2(mod i3)), the ceiling and floor functors (⌈x⌉ and ⌊x⌋), also the fraction part of a real number (frac), the integer division (÷) and remainder of integer division (mod). The following schemes were also included: the separation scheme (SepInt), the schemes of integer induction (Int Ind Down, Int Ind Up, Int Ind Full), the minimum (Int Min) and maximum (Int Max) schemes (the existence of minimum and maximum integers enjoying a given property).