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Topic: Is (t^2-9)/(t-3) defined at t=3?
Replies: 166   Last Post: Oct 30, 2013 9:41 AM

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 RGVickson@shaw.ca Posts: 1,677 Registered: 12/1/07
Re: Is (t^2-9)/(t-3) defined at t=3?
Posted: Sep 30, 2013 11:16 AM
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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.

Date Subject Author
9/28/13 Hetware
9/28/13 Michael F. Stemper
9/28/13 scattered
9/28/13 Hetware
9/28/13 quasi
9/28/13 Hetware
9/28/13 quasi
9/28/13 Peter Percival
9/29/13 quasi
9/28/13 Hetware
9/28/13 Richard Tobin
9/28/13 Hetware
9/28/13 tommyrjensen@gmail.com
9/29/13 Hetware
10/6/13 Hetware
10/6/13 Peter Percival
10/6/13 Hetware
10/6/13 quasi
10/8/13 quasi
10/7/13 Peter Percival
9/29/13 Michael F. Stemper
9/29/13 Hetware
9/29/13 quasi
9/29/13 Hetware
9/29/13 magidin@math.berkeley.edu
10/6/13 Hetware
10/6/13 magidin@math.berkeley.edu
10/7/13 Hetware
10/7/13 LudovicoVan
10/7/13 Peter Percival
10/8/13 magidin@math.berkeley.edu
10/12/13 Hetware
10/12/13 fom
10/13/13 magidin@math.berkeley.edu
10/13/13 Richard Tobin
10/13/13 Hetware
10/13/13 Peter Percival
10/13/13 fom
10/13/13 magidin@math.berkeley.edu
10/13/13 magidin@math.berkeley.edu
10/8/13 quasi
10/8/13 magidin@math.berkeley.edu
10/8/13 quasi
10/8/13 quasi
10/12/13 Hetware
10/13/13 quasi
10/13/13 Peter Percival
10/9/13 magidin@math.berkeley.edu
10/9/13 fom
10/10/13 magidin@math.berkeley.edu
10/10/13 fom
10/7/13 Peter Percival
10/7/13 Hetware
10/7/13 fom
10/7/13 Peter Percival
9/29/13 quasi
9/30/13 Peter Percival
9/30/13 Peter Percival
9/30/13 Peter Percival
9/30/13 RGVickson@shaw.ca
9/30/13 Roland Franzius
9/30/13 Richard Tobin
9/30/13 RGVickson@shaw.ca
9/28/13 Peter Percival
9/28/13 Hetware
9/29/13 Peter Percival
9/28/13 Virgil
9/29/13 quasi
9/29/13 Virgil
9/29/13 Hetware
9/29/13 quasi
9/29/13 Hetware
9/29/13 LudovicoVan
9/29/13 quasi
9/29/13 Virgil
9/29/13 magidin@math.berkeley.edu
9/29/13 Peter Percival
9/29/13 FredJeffries@gmail.com
9/30/13 Hetware
9/30/13 magidin@math.berkeley.edu
10/6/13 Hetware
10/6/13 Peter Percival
10/6/13 Peter Percival
10/6/13 magidin@math.berkeley.edu
10/6/13 Peter Percival
10/6/13 magidin@math.berkeley.edu
10/6/13 David Bernier
9/29/13 Peter Percival
9/28/13 Hetware
9/29/13 Richard Tobin
9/30/13 Ciekaw
9/30/13 Robin Chapman
9/30/13 Virgil
9/30/13 LudovicoVan
9/30/13 LudovicoVan
10/6/13 Hetware
10/7/13 Robin Chapman
10/7/13 David Bernier
10/7/13 Hetware
10/7/13 LudovicoVan
10/8/13 Hetware
10/9/13 Peter Percival
10/9/13 Richard Tobin
10/7/13 Peter Percival
10/8/13 Hetware
10/8/13 Virgil
10/8/13 Hetware
10/9/13 magidin@math.berkeley.edu
10/9/13 Peter Percival
10/10/13 Ciekaw
10/9/13 Peter Percival
10/10/13 Tim Golden BandTech.com
10/13/13 Hetware
10/13/13 Peter Percival
10/13/13 Hetware
10/14/13 Peter Percival
10/13/13 Hetware
10/13/13 fom
10/13/13 Hetware
10/13/13 fom
10/14/13 fom
10/14/13 Hetware
10/14/13 magidin@math.berkeley.edu
10/14/13 magidin@math.berkeley.edu
10/14/13 Peter Percival
10/14/13 Hetware
10/14/13 quasi
10/16/13 @less@ndro
10/16/13 quasi
10/19/13 Hetware
10/19/13 quasi
10/19/13 Hetware
10/20/13 fom
10/20/13 quasi
10/20/13 Hetware
10/20/13 fom
10/20/13 Hetware
10/20/13 Peter Percival
10/20/13 Richard Tobin
10/20/13 Hetware
10/30/13 @less@ndro
10/19/13 Hetware
10/10/13 Ronald Benedik
10/10/13 Peter Percival
10/10/13 Virgil
10/18/13 Hetware
10/19/13 Peter Percival
10/19/13 fom
10/19/13 Peter Percival
10/19/13 Hetware
10/19/13 Peter Percival
10/19/13 Hetware
10/19/13 fom
10/19/13 magidin@math.berkeley.edu
10/19/13 Hetware
10/19/13 magidin@math.berkeley.edu
10/20/13 Hetware
10/20/13 quasi
10/20/13 quasi
10/20/13 Hetware
10/20/13 Peter Percival
10/20/13 magidin@math.berkeley.edu
10/20/13 Hetware
10/20/13 Arturo Magidin
10/20/13 Hetware
10/20/13 magidin@math.berkeley.edu
10/19/13 fom

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