```Date: Sep 30, 2013 11:16 AM
Author: RGVickson@shaw.ca
Subject: Re: Is (t^2-9)/(t-3) defined at t=3?

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  <hattons@speakyeasy.net> 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.
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