Definition:Real Interval/Unbounded
< Definition:Real Interval(Redirected from Definition:Unbounded Real Interval)
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Definition
Unbounded Closed Interval
There are two unbounded closed intervals involving a real number $a \in \R$, defined as:
\(\ds \hointr a \to\) | \(:=\) | \(\ds \set {x \in \R: a \le x}\) | ||||||||||||
\(\ds \hointl \gets a\) | \(:=\) | \(\ds \set {x \in \R: x \le a}\) |
Unbounded Open Interval
There are two unbounded open intervals involving a real number $a \in \R$, defined as:
\(\ds \openint a \to\) | \(:=\) | \(\ds \set {x \in \R: a < x}\) | ||||||||||||
\(\ds \openint \gets a\) | \(:=\) | \(\ds \set {x \in \R: x < a}\) |
Unbounded Interval without Endpoints
The unbounded interval without endpoints is equal to the set of real numbers:
- $\openint \gets \to = \R$
Also known as
Some sources refer to these as infinite (real) intervals.
Also see
Sources
- 1970: Arne Broman: Introduction to Partial Differential Equations ... (previous) ... (next): Chapter $1$: Fourier Series: $1.1$ Basic Concepts: $1.1.1$ Definitions