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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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Peter Percival

Posts: 1,218
Registered: 10/25/10
Re: Is (t^2-9)/(t-3) defined at t=3?
Posted: Sep 28, 2013 4:30 PM
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Hetware wrote:

>>>> Hetware wrote:
>>>>>
>>>>> I'm reading a 1953 edition of Thomas's Calculus and Analytic
>>>>> Geometry.
>>>>>
>>>>> In it he states that given:
>>>>>
>>>>> F(t) = (t^2-9)/(t-3)
>>>>>
>>>>> F(t) = (t-3)(t+3)/(t-3) = t+3 when t!=3.
>>>>>
>>>>> [...]

> 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.


If F were a real-valued function on the reals, it might be defined thus:

( (t^2-9)/(t-3) for t=/=3
F(t) = (
( 6 for t=3

but if F is a real-valued function on R\{3} then there is no candidate
for F(3), obvious or otherwise.

Does your book call F a function? If so does it say what it's domain
is? Or is there a general rule for finding domains along the lines of
"most inclusive set of reals for which the expression makes sense"?


--
The world will little note, nor long remember what we say here
Lincoln at Gettysburg


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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Hetware
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quasi
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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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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
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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
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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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Richard Tobin
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Hetware
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Peter Percival
10/13/13
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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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quasi
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Peter Percival
10/9/13
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fom
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fom
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Hetware
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9/29/13
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Peter Percival
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Virgil
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Virgil
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Ciekaw
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10/13/13
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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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10/14/13
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10/14/13
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10/14/13
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Hetware
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10/16/13
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10/16/13
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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
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Hetware
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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
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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
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Arturo Magidin
10/20/13
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10/19/13
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