For questions about the structure, definition, and basic properties of the set of integers, or positive and negative whole numbers, commonly denoted $\mathbb{Z}$. Do not use this tag just because your question involves integers. Consider using (elementary-number-theory) or (number-theory) instead of or in addition to this tag.

The integers are the whole numbers, positive, negative and zero. That is, the integers are the numbers that appear in the infinite list

$$.\quad .\quad .\quad -5\quad -4\quad -3\quad -2\quad -1\quad 0\quad 1\quad 2\quad 3\quad 4\quad 5\quad .\quad .\quad .\quad$$

The set of all integers is denoted by $\mathbb{Z}$. The letter Z comes from the German word "Zahlen" which means "numbers". The integers are related to many other familiar sets of numbers:

$$\mathbb{N} \subset \mathbb{Z} \subset \mathbb{Q} \subset \mathbb{R} \subset \mathbb{C}.$$

The set of integers are closed under addition, subtraction, and multiplication. Together with the additive identity $0$ and the multiplicative identity $1$, the integers form an example of a commutative ring with unity. In fact, it is a Euclidean domain.