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Interval Notation

a way of writing the set of all real numbers between two endpoints. the symbols [ and ] are used to include an endpoint in an interval, and the symbols ( and ) are used to exclude an endpoint from an interval

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closed interval

denoted by [a,b] which contains all real numbers and a≤x≤b

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open interval

denoted by (a,b) which contains all real numbers x and a<x<b

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half open half closed intervals

are (a,b] consists of all real numbers x were a<x≤b, & [a,b) consists of all real numbers x were a≤x<b

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left endpoint

denoted by a

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right endpoint

denoted by b

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∞

infinity not a real number but a symbol that represents unboundedness in a positive direction; not included in endpoints since not a real number

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-∞

negative infinity not a real number but a symbol that represents unboundedness in a negative direction; not included in endpoints since not a real number

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[a,∞)

consists of all real numbers x for which x≥a

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(a,∞)

consists of all real numbers x for which x>a

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(-∞,a]

consists of all real numbers x for which x≤a

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(-∞,a)

consists of all real numbers x for which x<a

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(-∞,∞)

consists of all real numbers x

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a^2

any number squared is never a negative integer

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relation

correspondence between two sets

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x→y

x corresponds to y or y dends on x

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