## ::Extended real number line

### ::concepts

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In mathematics, the **affinely extended real number system** is obtained from the real number system ℝ 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 <math>\overline{\mathbb{R}}</math> 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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Infty::function Times::mathbb Number::topology Limit::defined Measure::value Overline::equal

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In mathematics, the **affinely extended real number system** is obtained from the real number system ℝ 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 <math>\overline{\mathbb{R}}</math> 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

PREVIOUS: Intro | NEXT: Motivation |

<< | >> |