Mel wrote:
John Yeung wrote:
And I accept your answer, as well as Steven's and Paul's for that
matter. I still think it is understandable (and people may choose to
understand in a condescending way, if they wish) that someone might
not get the difference between what you are saying and the statement
that all elements of the empty set are floats. I mean, what's in the
empty set? Nothing. But you've said that floats are something. How
is it that nothing is something?
It's sort of a logic equivalent of divide-by-zero.
All elements of the empty set are floats.
All elements of the empty set are ints.
Ints are not floats.
Therefore all elements of the empty set are not floats.
If
x in e => x in floats
x in e => x in ints
x in ints => x not in floats
Then
x in e => x not in floats, a contradition,
So
not(x in e), the definition of empty set.
You elaborate your logic to talk around this problem, and you quit when you
get tired.
No problem. Colloquial English is not the same as careful logic.
2 minutes, tired? Nah.
tjr
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