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About: Projectively extended real line     Goto   Sponge   NotDistinct   Permalink

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In real analysis, the projectively extended real line (also called the one-point compactification of the real line), is the extension of the set of the real numbers, by a point denoted ∞. It is thus the set with the standard arithmetic operations extended where possible, and is sometimes denoted by The added point is called the point at infinity, because it is considered as a neighbour of both ends of the real line. More precisely, the point at infinity is the limit of every sequence of real numbers whose absolute values are increasing and unbounded.