Extended real number line – Wikipedia, the free encyclopedia

Extended real number line

via Extended real number line – Wikipedia, the free encyclopedia.

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). The projective extended real number system adds a single object, ∞ (infinity) and makes no distinction between “positive” or “negative” infinity. 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 R or [−∞, +∞].

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

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