Tour:Group of integers

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

This page is part of the Groupprops guided tour for beginners (Jump to beginning of tour)
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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, -).

This page is part of the Groupprops guided tour for beginners. Make notes of any doubts, confusions or comments you have about this page before proceeding.
PREVIOUS: Isomorphic groups| UP: Introduction four (beginners)| NEXT: Group of integers modulo n
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