Re: Question about null set

In article <K52le.19376$tM3.4604@xxxxxxxxxxxxxxxxxxxx>,
Justin Young <x_static66@xxxxxxxxxxx> wrote:
><agapito6314@xxxxxxx> wrote in message
>news:1117037867.118257.154940@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
>>I believe I understand why the empty set is a set of ordered pairs,
>> vacuously: the statement "for all x, if x belongs to empty set then x
>> is an ordered pair" is always true.
>
>this is sufficient to prove that the empty set is a set of ordered pairs.
>i see no need to use a proof by contradiction.

A lot of people have trouble "getting" that universal statements
quantified over the empty set are always true. The 'usual' way to make
the idea click for most is to argue by contrapositive (which may look
like a proof by contradiction; a lot of people phrase
contrapositive proofs as if they were proofs by contradiction).

--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes")
======================================================================

Arturo Magidin
magidin@xxxxxxxxxxxxxxxxx

.

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