On Tue, Oct 15, 2002 at 04:07:51PM -0700, [EMAIL PROTECTED] wrote:
> [1]: This comes from a recent discussion on perlmonks where i attempted
> to formally iron things out for people, since i have yet to see anywhere
> thus far on the web where it was actually formalized.
> (formalization being markedly different from rationalization)
> http://www.perlmonks.org/index.pl?node_id=203698
Here's two simple proofs by contradiction.
Let 1/0 == +Infinity
Then 1 == +Infinity * 0
Since anything times 0 == 0
1 == 0
Contradiction.
Here's another way to look at it.
0 * 1/0 == ?
On the one hand, anything times 0 == 0. So it's 0.
On the other hand, a * b/a == b. So it's 1.
Contradiction.
I don't know exactly what you're looking for in terms of formal proofs,
but the above math will hold just fine.
For more a more complete analysis of what happens when you try to
introduce infinity into the real number system, see:
http://mathforum.org/library/drmath/view/55764.html
--
Michael G. Schwern <[EMAIL PROTECTED]> http://www.pobox.com/~schwern/
Perl Quality Assurance <[EMAIL PROTECTED]> Kwalitee Is Job One
This is my sig file. Is it not nify? Worship the sig file.
http://www.sluggy.com
