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@Thalesdisciple Many formulas about intervals which fail for points should probably be rewritten to say "open interval".On twitter.com
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@Thalesdisciple er, TFW you notice @siwelwerd beat you to the same point. D-:Permalink On twitter.com
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@Thalesdisciple e.g. the Cantor set contains no open intervals. Topologically this is better anyway: it's a nowhere dense set.Permalink On twitter.com
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@Thalesdisciple e.g. if f is constant on an open interval, then f'=0 on that interval.Permalink On twitter.com
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@Thalesdisciple Actually that fact is false for the endpoints anyway: the derivative could be 0 or undefined.Permalink On twitter.com