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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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Hetware

Posts: 148
Registered: 4/13/13
Re: Is (t^2-9)/(t-3) defined at t=3?
Posted: Sep 29, 2013 8:30 PM
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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


Date Subject Author
9/28/13
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Hetware
9/28/13
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Michael F. Stemper
9/28/13
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scattered
9/28/13
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Hetware
9/28/13
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quasi
9/28/13
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Hetware
9/28/13
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quasi
9/28/13
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Peter Percival
9/29/13
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quasi
9/28/13
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Hetware
9/28/13
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Richard Tobin
9/28/13
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Hetware
9/28/13
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tommyrjensen@gmail.com
9/29/13
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Hetware
10/6/13
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Hetware
10/6/13
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Peter Percival
10/6/13
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Hetware
10/6/13
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quasi
10/8/13
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quasi
10/7/13
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Peter Percival
9/29/13
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Michael F. Stemper
9/29/13
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Hetware
9/29/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
quasi
9/29/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Hetware
9/29/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
magidin@math.berkeley.edu
10/6/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Hetware
10/6/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
magidin@math.berkeley.edu
10/7/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Hetware
10/7/13
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LudovicoVan
10/7/13
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Peter Percival
10/8/13
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magidin@math.berkeley.edu
10/12/13
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Hetware
10/12/13
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fom
10/13/13
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magidin@math.berkeley.edu
10/13/13
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Richard Tobin
10/13/13
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Hetware
10/13/13
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Peter Percival
10/13/13
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fom
10/13/13
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magidin@math.berkeley.edu
10/13/13
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magidin@math.berkeley.edu
10/8/13
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quasi
10/8/13
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magidin@math.berkeley.edu
10/8/13
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quasi
10/8/13
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quasi
10/12/13
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Hetware
10/13/13
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quasi
10/13/13
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Peter Percival
10/9/13
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magidin@math.berkeley.edu
10/9/13
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fom
10/10/13
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magidin@math.berkeley.edu
10/10/13
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fom
10/7/13
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Peter Percival
10/7/13
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Hetware
10/7/13
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fom
10/7/13
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Peter Percival
9/29/13
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quasi
9/30/13
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Peter Percival
9/30/13
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Peter Percival
9/30/13
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Peter Percival
9/30/13
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RGVickson@shaw.ca
9/30/13
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Roland Franzius
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Richard Tobin
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9/28/13
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Peter Percival
9/28/13
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Hetware
9/29/13
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Peter Percival
9/28/13
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Virgil
9/29/13
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quasi
9/29/13
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Virgil
9/29/13
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Hetware
9/29/13
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quasi
9/29/13
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Hetware
9/29/13
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LudovicoVan
9/29/13
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quasi
9/29/13
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Virgil
9/29/13
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magidin@math.berkeley.edu
9/29/13
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9/29/13
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9/30/13
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Hetware
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magidin@math.berkeley.edu
10/6/13
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Hetware
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10/6/13
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Peter Percival
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magidin@math.berkeley.edu
10/6/13
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Peter Percival
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magidin@math.berkeley.edu
10/6/13
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David Bernier
9/29/13
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9/28/13
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Hetware
9/29/13
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9/30/13
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Ciekaw
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Robin Chapman
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LudovicoVan
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10/6/13
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Hetware
10/7/13
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Hetware
10/7/13
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10/8/13
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Hetware
10/9/13
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10/9/13
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Richard Tobin
10/7/13
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10/8/13
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Hetware
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Virgil
10/8/13
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Hetware
10/9/13
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magidin@math.berkeley.edu
10/9/13
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Peter Percival
10/10/13
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Ciekaw
10/9/13
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10/10/13
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Tim Golden BandTech.com
10/13/13
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Hetware
10/13/13
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Peter Percival
10/13/13
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Hetware
10/14/13
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Peter Percival
10/13/13
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Hetware
10/13/13
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fom
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Hetware
10/13/13
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fom
10/14/13
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fom
10/14/13
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Hetware
10/14/13
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magidin@math.berkeley.edu
10/14/13
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magidin@math.berkeley.edu
10/14/13
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Peter Percival
10/14/13
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Hetware
10/14/13
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quasi
10/16/13
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@less@ndro
10/16/13
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quasi
10/19/13
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Hetware
10/19/13
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quasi
10/19/13
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Hetware
10/20/13
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fom
10/20/13
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quasi
10/20/13
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Hetware
10/20/13
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fom
10/20/13
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Hetware
10/20/13
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Peter Percival
10/20/13
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Richard Tobin
10/20/13
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Hetware
10/30/13
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@less@ndro
10/19/13
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Hetware
10/10/13
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Ronald Benedik
10/10/13
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Peter Percival
10/10/13
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Virgil
10/18/13
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Hetware
10/19/13
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Peter Percival
10/19/13
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fom
10/19/13
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Peter Percival
10/19/13
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Hetware
10/19/13
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Peter Percival
10/19/13
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Hetware
10/19/13
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fom
10/19/13
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magidin@math.berkeley.edu
10/19/13
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Hetware
10/19/13
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magidin@math.berkeley.edu
10/20/13
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Hetware
10/20/13
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quasi
10/20/13
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quasi
10/20/13
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Hetware
10/20/13
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Peter Percival
10/20/13
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magidin@math.berkeley.edu
10/20/13
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Hetware
10/20/13
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Arturo Magidin
10/20/13
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Hetware
10/20/13
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magidin@math.berkeley.edu
10/19/13
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fom

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