Tour:Group of integers

This article adapts material from the main article: group of integers

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WHAT YOU NEED TO DO: Read and understand the definition of the group of integers.

Definition

Usual definition

The group of integers, typically denoted $\mathbb{Z}$, is defined as follows:

• The underlying set is the set of all integers
• The group operation is integer addition
• The identity element is the integer $0$
• The inverse map is the additive inverse, sending an integer $n$ to the integer $-n$

In the 4-tuple notation, the group of integers in the group $(\mathbb{Z},+, 0, -)$.

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