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Concept

An interval consisting of real numbers contains an infinite amount of numbers. In the interval $1≤x≤4,$ all numbers between $1$ and $4$ are part of the set. For example, $1,$ $2.7,$ $3.5,$ $3.61,$ and $4.$
An interval does not have to be limited between two ends. For example, the inequality $x≥0$ is the set of *all* positive real numbers greater than or equal to $0.$

Interval notation is a way to denote an interval. In this notation, a square bracket, $[$ or $],$ is used when the end value is *included*, and a round bracket, $($ or $),$ is used when the end value is *not* included. When using interval notation, the left value is less than the right value.

Interval Notation | Description | Type of Interval |
---|---|---|

$(a,b)$ | Both ends are not included | Open interval |

$[a,b]$ | Both ends are included | Closed interval |

$[a,b)$ or $(a,b]$ | One end is not included | Half-open interval |

Note that if the variable only has one limit, the other is infinity, $∞$ or $-∞,$ and is

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