Definition:Real Interval/Unbounded

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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