Hetware wrote: > >What I am saying is that if I encountered an expression such >as (t^2-9)/(t-3) in the course of solving a problem in >applied math, I would not hesitate to treat it as t+3 and not >haggle over the case where t = 3.
And you would be wrong unless either
(1) You know by the context of the application that the value t = 3 is impossible.
(2) You know by the context that the underlying function must be continuous, thus providing justification for canceling the common factor of t-3, effectively removing the discontinuity.
I challenged you to find a book -- _any_ book, which agrees with your naive preconception.
Math book, applied math book, physics book, chemistry book, economics book -- whatever.
If all the books and all the teachers say you're wrong, don't you think that maybe it's time to admit that you had a flawed conception about this issue and move on?