Thread View: k12.ed.math
2 messages
2 total messages
Started by Mike Bolduan
Thu, 21 Jan 1993 17:41
Re: INTEGRALS
Author: Mike Bolduan
Date: Thu, 21 Jan 1993 17:41
Date: Thu, 21 Jan 1993 17:41
41 lines
1866 bytes
1866 bytes
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. 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. If I had read a bit more about improper integrals I would have quickly found the part that defines the "sum" of two integrals as divergent if EITHER (or both) of the integrals which make it up are divergent. This is the case here, so: end of story. The integral of 1/x from -1 to 1 is divergent and NOT ZERO. Sometimes "common sense" takes it in the ear... :-) 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!) Looks like I got folks thinking a bit. Neat-O mike bolduan@catseq.catlin.edu internet bolduan@catlin bitnet -- mike bolduan bolduan@catlin
Re: INTEGRALS
Author: I am a terminator.
Date: Mon, 25 Jan 1993 16:55
Date: Mon, 25 Jan 1993 16:55
52 lines
2661 bytes
2661 bytes
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
Thread Navigation
This is a paginated view of messages in the thread with full content displayed inline.
Messages are displayed in chronological order, with the original post highlighted in green.
Use pagination controls to navigate through all messages in large threads.
Back to All Threads