Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Hetware

Posts: 148
Registered: 4/13/13
Re: Is (t^2-9)/(t-3) defined at t=3?
Posted: Sep 28, 2013 6:14 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 9/28/2013 4:30 PM, Peter Percival wrote:
> 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"?
>
>


F(t) is called a function of t, but his definition of a function doesn't
preclude my considering (t^2-9)/(t-3) as being synonymous with (t + 3).
He gives (t^2-9)/(t-3) as an example of a function which is undefined
at t = 3, but has a limit as t -> 3.

If it's the rules 'cause it's the rules, so be it. I just don't see a
logical necessity for precluding t = 3 from the domain of F(t). If I
choose to interpret (t-3)/(t-3) = 1 for all real numbers, I don't see
how it results in a logical contradiction.

The rule Thomas is following is that evaluating (t^2-9)/(t-3) for a
given value of t means evaluating each sub-expression "as is". If we
had a rule that evaluating an algebraic expression means evaluating its
simplest form, how would it change the results of mathematics?




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

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.