Definition:Limit Point/Real Analysis
< Definition:Limit Point(Redirected from Definition:Limit Point (Real Analysis))
Jump to navigation
Jump to search
Definition
Let $S \subseteq \R$ be a subset of the real numbers.
Let $\xi \in \R$ and let $S_\xi$ be the set defined as:
- $S_\xi := \set {x: x \in S, x \ne \xi}$
Then $\xi$ is a limit point of $S$ if and only if $\xi$ is at zero distance from $S_\xi$.
Sources
- 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 5.21 \ (6)$