Group of real numbers

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VIEW FACTS ABOUT THIS GROUP: All factsGroup property satisfactionsSubgroup property satisfactionsGroup property dissatisfactionsSubgroup property satisfactions
VIEW DEFINITIONS USING THIS AS EXAMPLE: All terms |Group properties |Subgroup properties|
VIEW FACTS USING THIS AS EXAMPLE: All facts |Group property non-implications |Subgroup property non-implications |Group metaproperty dissatisfactionsSubgroup metaproperty dissatisfactions

Definition

The group of real numbers, also called the additive group of real numbers, is denoted as $\mathbb {R}$, and is defined as follows:

It is the group whose elements are real numbers, the group operation is addition of real numbers, the identity element is zero, and the inverse is the negative. In the tuple notation, it is written as $(\mathbb {R} ,+,0,-)$.

Important subgroups

• The group of rational numbers
• The group of integers