> In that case, you are wrong on two problems for the price of one.
My copy of
> Rudin is at my office, so it's not in front of me, but the vacuous
proof of
> being closed is absolutely correct.
I couldn't find the word "vacuously" anywhere in Rudin, which is why
I asked for clarification. Apparently, it is mathematician
for "trivially" (which itself is mathematician for "actually really
hard," in my experience). Also, I didn't say it was wrong, just that
I didn't believe a word of it, just like I don't really believe
anything I learned in analysis because I think it is all a great big
wad of lies concocted by crazy mathematicians in order to confuse
normal people :).
> As for your second mistake, a countable set can easily be
compact. The
> simplest example is to take your own example {1, 1/2, 1/3, etc}
and add the
> single point {0} to the set.
It wasn't my example, but thank you for it anyway.
Jerry