🚀 go-pugleaf

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



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mike bolduan
bolduan@catlin