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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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FredJeffries@gmail.com

Posts: 1,107
Registered: 11/29/07
Re: Is (t^2-9)/(t-3) defined at t=3?
Posted: Sep 29, 2013 6:29 PM
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On Saturday, September 28, 2013 1:15:47 PM UTC-7, Hetware wrote:
>
> So the answer is consensus among mathematicians holds that F(t) = (t^2 -
> 9)/(t - 3) is undefined at t=3? 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.


But you are not setting up an equation in physics. You are
attempting to learn calculus.

Professor Thomas has a very good reason for showing you this
trivial-seeming example of a function with what is known
as a "removable singularity". If you are patient and continue
to study his book you will find his reasons. Here's a hint:
the function sin(x)/x has the same feature at x = 0.

>
> If I conceive of mathematics as an exercise in defining and manipulating
> symbols, it seems that declaring constructs such as F(t) = (t^2 - 9)/(t
> - 3) to be undefined at t=3 is arbitrary. The fact that there is an
> obvious candidate for a value of F(t) at t=3 tells me that accepting
> that candidate as the value at t=3 does not contradict the definition of
> a single valued function of one variable.


Of course it does not contradict the definition of a single valued
function of one variable. It contradicts the definition of one
particular function, namely Professor Thomas's F(t). The fact that
this all seems totally arbitrary to you is just because you
don't know the whole story yet.


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
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Hetware
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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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10/8/13
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Peter Percival
9/29/13
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Michael F. Stemper
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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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magidin@math.berkeley.edu
10/6/13
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Hetware
10/6/13
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magidin@math.berkeley.edu
10/7/13
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Hetware
10/7/13
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LudovicoVan
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Peter Percival
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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
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Hetware
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Peter Percival
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fom
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magidin@math.berkeley.edu
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quasi
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quasi
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Peter Percival
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10/9/13
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fom
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fom
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Hetware
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fom
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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
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9/29/13
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Virgil
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Virgil
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LudovicoVan
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quasi
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Hetware
10/9/13
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Hetware
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10/9/13
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Peter Percival
10/10/13
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Ciekaw
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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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10/13/13
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10/14/13
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10/13/13
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Hetware
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Hetware
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10/14/13
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fom
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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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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
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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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Hetware
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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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10/19/13
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