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All those numbers which lie between two specific numbers.
All those points which lie between two specific points along a line.

Any subset I ⊆ R satisfying x ≤ y ≤ z     and x,z ∈ I \implies y ∈ I .
There are nine different forms of interval, classified according to whether the interval in unbounded at either end, or either of the `endpoints' are in the set or not.
See also connected.