Bounded and Whole Interval

3.1.4 Bounded and Whole Interval

An interval $X ∈IR$ is considered to be bounded if $- x,x∈R$ and are finite. If either but not both of $x$ or $- x$ are $± ∞$ with the respective sign the interval is considered to be a lower bounded or upper unbounded interval.

If $x= -∞$ and $- x= ∞$ the interval spans the whole $x∈ R$ space, this is called a whole interval.

A special case is $- x= x= ∞$ which is by definition an empty interval, as there will be no elements in the resulting interval set.

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