firstname.lastname@example.org (Jesse F. Hughes) wrote: > Eckard Blumschein <email@example.com> writes: > > > Robin Chapman wrote: > > > >>>I realized: An empty set is known to be neither open nor closed, of > >>>course. > >> > >> > >> ! > > > > http://mathworld.wolfram.com/EmptySet.html > > > > Well, they did not write "neither not" but "both" open and closed. > > Since open and close contradict each other, I was just a bit sloppy. > > But the topological notions don't contradict each other at all. > > I'm not sure that I'd call your statement above "just a bit sloppy". > If X and Y are true, then asserting "NOT X and NOT Y" is more than a > bit sloppy. > > > I merely do not understand why they wrote "strangely". > > Me either.
I suspect I do: Eric Weisstein wrote "strangely" because the words "open" and "closed" _seem_, based on their extramathematical meanings, to contradict each other.