Terry Reedy tjreedy at udel.edu
Mon Jun 15 01:27:46 CEST 2009

```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

```