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 set of the real numbers, R {\displaystyle \mathbb {R} } , by a point denoted ∞. It is thus the set R ∪ { ∞ } {\displaystyle \mathbb {R} \cup \{\infty \}} with the standard arithmetic operations extended where possible, and is sometimes denoted by R ∗ {\displaystyle \mathbb {R} ^{*}} or R ^ .

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