Definition:Real Interval/Half-Open
Contents
Definition
Let $a, b \in \R$.
There are two half-open (real) intervals from $a$ to $b$.
Right half-open
The right half-open (real) interval from $a$ to $b$ is the subset:
- $\hointr a b := \set {x \in \R: a \le x < b}$
Left half-open
The left half-open (real) interval from $a$ to $b$ is the subset:
- $\hointl a b := \set {x \in \R: a < x \le b}$
Also known as
This can often be seen rendered as half open interval.
Examples
Example $1$
Let $I$ be the unbounded closed real interval defined as:
- $I := \hointr 1 2$
Then $1 \in I$.
Also see
- Definition:Open Real Interval
- Definition:Closed Real Interval
- Definition:Unbounded Open Real Interval
- Definition:Unbounded Closed Real Interval
- Definition:Half-Open Rectangle, a generalization to higher dimensional spaces
Sources
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- 1983: George F. Simmons: Introduction to Topology and Modern Analysis ... (previous) ... (next): $\S 1$: Sets and Set Inclusion
