Hetware wrote: >quasi wrote: >> 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? > >I don't answer to the authority of mortals. I answer to the >dictates of reason.
That declaration doesn't bode well for success if your goal is to gain a high level understanding of Calculus.
It also makes clear that you have little respect for the wisdom and intellect of the tens of thousands of mathematicians, past and present, who have also reasoned about this issue, and are essentially unanimous in their agreement as to how the issue should be dealt with.
Have you convinced anyone else yet?
So your reasoning has such a degree of certainty in your mind that it trumps reasoning by all others?
Said differently, when you consider the chance that you might be wrong versus the chance that everyone else is wrong, you have no doubt that _you_ have it right and _they_ have it wrong?
Humble you're not.
Is it your depth of knowledge that gives you such confidence to be so absolutely sure everyone else is wrong? But it seems you don't yet even know Calculus. So much for depth of knowledge.