Projectively extended real line

In real analysis, the projectively extended real line (also called the one-point compactification of the real line), is the extension of the number line by a point denoted ∞. It is thus the set ${\displaystyle \mathbb {R} \cup \{\infty \}}$ (where ${\displaystyle \mathbb {R} }$ is the set of the real numbers) with the standard arithmetic operations extended where possible, sometimes denoted by ${\displaystyle {\widehat {\mathbb {R} }}.}$ 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.

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