David C. Ullrich wrote:
In article <[EMAIL PROTECTED]>,
Ken Starks <[EMAIL PROTECTED]> wrote:
David C. Ullrich wrote:
I don't see why you feel the two should act the same.
At least in mathematics, the sum of the elements of
the empty set _is_ 0, while the maximum element of the
empty set is undefined.
And both for good reason:
(i) If A and B are disjoint sets we certainly want to
have sum(A union B) = sum(A) + sum(B). This requires
sum(empty set) = 0.
(ii) If A is a subset of B then we should have
max(A) <= max(B). This requires that max(empty set)
be something that's smaller than everything else.
So we give up on that.
Do we give up? Really ?
Erm, thanks. I was aware of all that below. If we're
being technical what's below is talking about the sup
and inf, which are not the same as max and min. More
relevant to the present context, I didn't mention what's
below because it doesn't seem likely that saying max([])
= -infinity and min([]) = +infinity is going to make the
OP happy...
Of course you were aware, I have seen enough of your posts
to know that. And I agree that, whatever Wikipedia seems to
imply, max and supremum should be distiguished.
It was your prelude, "At least in mathematics ..." that
made me prick up my ears. So I couldn't resist responding,
without _any_ malice I assure you.
Cheers,
Ken.
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