The projectively extended real line is the set of real numbers together with a single point at infinity approached from both the positive and negative directions, making it topologically a circle rather than a line. This differs from the two-point extension of the reals used in ordinary extended real analysis, which adds separate positive and negative infinities. The projective extension is used in projective geometry and in certain branches of complex analysis and calculus where arithmetic operations such as division by zero can be given a consistent, if degenerate, meaning by treating infinity as a single unsigned point.
Facts
Connections
In Branch
Source Projectively Extended Real Line (Wikipedia)
Is Kind Of Object
Sources
1. Projectively Extended Real Line (Wikipedia)
Lead section
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
In Branch: Real Analysis, Lead sentence
In real analysis, the projectively extended real line (also called the one-point compactification of the real line), is the extens
View the SourceReader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.