🚀 go-pugleaf

In article <1jmn8cINN3n9@usenet.INS.CWRU.Edu>, cb919@cleveland.Freenet.Edu (Mike Bolduan) writes:
|> 
|> David Radcliffe:
|> 
|> YES!!!!
|> You said it much better than I could have. It is a matter of 
|> definition and a definition is "what we say it is". We have the 
|> right to define anything we want in any way we wish. It is a 
|> "bad" definition (and hence should probably not have been 
|> made) if it leads to "nastiness" (e.g., contradictions) down the 
|> road.

The definition may not be so bad. It get's us away from a lot of
trouble (see <1jkfe8INN7ou@access.usask.ca>). How can you >> verify <<
the limit to be zero when it heads to -infinity coming from the left
and to +infinity coming from the right?

|> This reminds me just a tad about the huge debate a couple of 
|> years ago about the meaning of 0^0. (and please let's just let 
|> sleeping dogs lie!)This also is a matter of how we wish to 
|> define something.

Hmm. What can you do? Consider lim x->0 0^x. Then consider
lim x->0 x^0. Then consider the definition of exponentiation.
a^x means exp(x ln a). But ln x is not defined at x=0 !

|> BTW I would highly recommend a couple of books for 
|> people interested in calculus as it (should) be taught these 
|> days:
|> 1) The new material by the Harvard Consortium published 
|> by Wiley
|> 2) The book by Dick and Patton which integrates (sorry 
|> 'bout that!   :-))  technology into the class)
|> 3) Calculus by Gilbert Strang which is a VERY interesting 
|> book (although 'tain't cheap!)

I really like Modern Calculus and Analytic Geometry by R.A. Silverman.
I got it used for $8. It looked like new though, so I pity the previous
owner.

-- 

Henry Choy
choy@cs.usask.ca

What rolls down stairs alone or in pairs            This has been brought to 
Rolls over your neighbor's dog?                     you by the numbers 4
What's great for a snack and fits on your back?     and 9 and the letter P.
It's Log, Log, Log!  -- "The Log Song", from            -- Big Bird
                         Ren & Stimpy

Math is tough!       -- Barbie