## ::Extended real number line

### ::concepts

Infty::function    Times::mathbb    Number::topology    Limit::defined    Measure::value    Overline::equal

{{#invoke:redirect hatnote|redirect}} {{ safesubst:#invoke:Unsubst||$N=Refimprove |date=__DATE__ |$B= {{#invoke:Message box|ambox}} }} In mathematics, the affinely extended real number system is obtained from the real number system by adding two elements: + ∞ and – ∞ (read as positive infinity and negative infinity respectively). These new elements are not real numbers. It is useful in describing various limiting behaviors in calculus and mathematical analysis, especially in the theory of measure and integration. The affinely extended real number system is denoted $\overline{\mathbb{R}}$ or [–∞, +∞] or ℝ ∪ {–∞, +∞}.

When the meaning is clear from context, the symbol +∞ is often written simply as .

Extended real number line sections
Intro  Motivation  Order and topological properties  Arithmetic operations  Algebraic properties  Miscellaneous  See also  References

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