# Real Number

## Real Number

Number that, when written in decimal notation, is an unlimited decimal sequence periodic or not.

### Notations

• The symbol that represents the set of real numbers is the letter $$\mathbb{R}$$.
• The symbol that represents the set of real positive numbers is: $$\mathbb{R}_{+}$$ = {x ∈ $$\mathbb{R}$$ | x ≥ 0}
• The symbol that represents the set of real negative numbers is:$$\mathbb{R}_{–}$$ = {x ∈ $$\mathbb{R}$$ | x ≤ 0}
• The symbol that represents the set of the non-zero real numbers is: $$\mathbb{R}{^*}$$ = {x ∈ $$\mathbb{R}$$ | x ≠ 0}
• The symbol that represents the set of strictly positive real numbers is: $$\mathbb{R}_{+}^{*}$$ = {x ∈ $$\mathbb{R}$$ | x > 0}
• The symbol that represents the set of strictly negative real numbers is: $$\mathbb{R}_{–}^{*}$$ = {x ∈ $$\mathbb{R}$$ | x < 0}

The set $$\mathbb{R}$$ of real numbers appears in this Venn diagram: