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Real numbers/Intervals/Definition
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Real numbers
Real intervals
For real numbers
a
,
b
{\displaystyle {}a,b}
,
a
≤
b
{\displaystyle {}a\leq b}
, we call
[
a
,
b
]
=
{
x
∈
R
∣
x
≥
a
and
x
≤
b
}
{\displaystyle {}[a,b]={\left\{x\in \mathbb {R} \mid x\geq a{\text{ and }}x\leq b\right\}}}
the
closed interval
.
]
a
,
b
[
=
{
x
∈
R
∣
x
>
a
and
x
<
b
}
{\displaystyle {}]a,b[={\left\{x\in \mathbb {R} \mid x>a{\text{ and }}x<b\right\}}}
the
open interval
.
]
a
,
b
]
=
{
x
∈
R
∣
x
>
a
and
x
≤
b
}
{\displaystyle {}]a,b]={\left\{x\in \mathbb {R} \mid x>a{\text{ and }}x\leq b\right\}}}
the
half-open interval
(closed on the right).
[
a
,
b
[
=
{
x
∈
R
∣
x
≥
a
and
x
<
b
}
{\displaystyle {}[a,b[={\left\{x\in \mathbb {R} \mid x\geq a{\text{ and }}x<b\right\}}}
the
half-open interval
(closed on the left).
, 
,
we call
![{\displaystyle {}[a,b]={\left\{x\in \mathbb {R} \mid x\geq a{\text{ and }}x\leq b\right\}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/527085bb43c88d9d49559f105a9268740b897342)
the closed interval.
![{\displaystyle {}]a,b[={\left\{x\in \mathbb {R} \mid x>a{\text{ and }}x<b\right\}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d20bb8e8877b250e1c747523615c37c4796c2105)
the open interval.
![{\displaystyle {}]a,b]={\left\{x\in \mathbb {R} \mid x>a{\text{ and }}x\leq b\right\}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/30143282fcf8fbf33bf99a4850ec61d3ca8a1477)
the half-open interval (closed on the right).
the half-open interval (closed on the left).
