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The interval [0,1] is compact because every infinite subset of it has a limit point that remains inside [0,1]. For example, the subset {$1/n$} accumulates at 0, and since the interval is closed, 0 is included in [0,1].

Conditions: E is the closed interval [0,1].; Compactness is judged by Hausdorff's limit-point definition.; S is an infinite subset of [0,1].

The interval [0,1] is compact because every infinite subset of it has a limit point that remains inside [0,1]. For example, the subset {$1/n$} accumulates at 0, and since the interval is closed, 0 is included in [0,1].

Conditions: E is the closed interval [0,1].; Compactness is judged by Hausdorff's limit-point definition.; S is an infinite subset of [0,1].