> I suspect I do: Eric Weisstein wrote "strangely" because the words "open" > and "closed" _seem_, based on their extramathematical meanings, to > contradict each other.
Isn't the mathematical meaning: Zero is included as well as excluded? This is exactly what I am trying to suggest for any infinitely precise real, not just for zero. If a frontier stone of zero dimensions is immediately surrounded by infinitely much of very similar stuff, then its removal or the opposite does not matter at all. I suspect: Included and excluded do contradict in mathematics too, unless they refer to something infinitesmal small.