Integers

The integers are the natural numbers \(0, 1, 2, 3, \dots\) and their opposites \(-1, -2, -3, \dots\). Their set is written \(\mathbb{Z}\):

\[ \mathbb{Z} = \{\dots, -3, -2, -1, 0, 1, 2, 3, \dots\} \]

• Closed under addition, subtraction and multiplication. The sum, difference and product of two integers are always integers. The quotient need not be: \(1 \jako 2\) is not an integer.
• Order. On the number line every integer has a next integer and a previous one, and there are no other integers between two consecutive integers.
• Part of larger sets. Every integer is a rational number, because \(n = \frac{n}{1}\).