Date: Sep 30, 2013 1:21 PM
Author: RGVickson@shaw.ca
Subject: Re: Is (t^2-9)/(t-3) defined at t=3?
On Sunday, September 29, 2013 5:30:49 PM UTC-7, Hetware wrote:

> On 9/29/2013 8:06 PM, 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?

>

> >

>

> > quasi

>

> >

>

>

>

> I don't answer to the authority of mortals. I answer to the dictates of

>

> reason. I say that it is logically consistent to view

>

>

>

> (t^2-9)/(t-3) = t+3

>

>

>

> as valid when t = 3. If a contradiction can be demonstrated, then the

>

> proposition is clearly wrong. Note clearly that I am defining

>

> (t-3)/(t-3)=1. I am not appealing to a more fundamental meaning for the

>

> algebraic form.

>

>

>

> I can't show you a book that explicitly tells me I can do this, but I

>

> can cite one that tells me that I can get away with it, until you prove

>

> a contradiction:

>

> http://books.google.com/books/about/Grundz%C3%BCge_Der_Mathematik_Fundamentals_o.html?id=1N0lMwEACAAJ

So, logically, you know what is the value of f = 0/0? According to the definition of division ('/'), f is that number which, when multiplied by the denominator (0 in this case) gives the numerator (also 0 in this case). So, you want an f that gives you 0*f = 0. That is the DEFINITION of division! (If you insist on being logical, you should insist on starting with the definition.) So, tell me: what is the value of f, and why do you claim that value?