On Saturday, September 28, 2013 2:20:58 PM UTC-7, Hetware wrote: > On 9/28/2013 4:24 PM, Richard Tobin wrote: > > > In article <9cSdnYGhH7CMpNrPnZ2dnUVZ_sCdnZ2d@megapath.net>, > > > Hetware <email@example.com> wrote: > > > > > >> So the answer is consensus among mathematicians holds that F(t) = (t^2 - > > >> 9)/(t - 3) is undefined at t=3? > > > > > > Yes. > > > > > >> Perhaps what I should have said at the > > >> outset is something along the lines of: on any given day, if I'm setting > > >> up an equation in physics, and produce an expression such as F(t) = (t^2 > > >> - 9)/(t - 3), I treat it as t+3, and do not expect any adverse > > >> consequence from doing so. > > > > > > Your simplification is not valid for t=3. If there is a real > > > physical interpretation, perhaps you can derive the formula t+3 > > > without going through the intermediate form (t^2-9)/(t-3). Or > > > consider the special case t=3 to show that the result is indeed > > > t+3 in that case too. > > > > > > In fact, I would be interested to see a physical problem where you > > > can't do that. > > > > > > -- Richard > > > > > > > I believe most mathematicians solving for x as a function of t given > > > > t^2 - 9 = x (t - 3) > > > > would not hesitate to factor the left hand side and divide both sides by > > t - 3 without treating t = 3 as a special case. Doing so repeats the > > sin of dividing by zero twice. We can certainly solve > > > > t^2 - 9 = 6 (t - 3) > > > > without dividing by zero which seems to justify our implied sin.
Your belief is incorrect: many beginning students would not hesitate to find the solution x = t+3, but no competent mathematician would do so without qualification. Being sloppy like that is exactly why some students get incorrect answers to perfectly well-defined questions in areas like constrained optimization, for example. Often one encounters such equations---not as the result of 'trickery' or for the sake of trying to construct artificial difficulties---but as a natural outcome during the analysis of certain types of problems. Good software developers build in safeguards against such exceptional cases, thus avoiding the so-called 'bugs' that another poster has falsely claimed applies here.