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: Oct 20, 2013 3:54 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 10/20/2013 4:07 PM, quasi wrote:
> Hetware wrote:
>>
>> So Quasi was correct.

>
> Of course!
>
> (just kidding)
>

>> I can define a function g(x) to be continuous,
>
> I don't think I said that.


Someone agreed with me that a function can be defined as continuous.

> Let's try a similar example with a change of wording:
>
> Let h be a continuous function such that
>
> h(x) = f(x) for x != 3
>
> Does the above qualify as a "definition" of h?
>
> For the above to be regarded as a definition, it must be the
> case that there is one and only one function h which satisfies
> the above conditions. But you would first have to _prove_ that
> claim. Only then can you claim to have "defined" h.
>
> In other words, imposing conditions on h is not the same as
> defining h.


What I intend by defining a function to be continuous is to remove all
removable discontinuities resulting from the (other) rules given. We
are always obliged to determine that the definition proposed does indeed
satisfy the properties of a function as well as consistency. So if we
proposed a definition which asserted continuity, and other rules of the
function resulted in an irremovable discontinuity, the proposed function
would be invalid.

> Now consider a sample test problem ...
>
> Suppose k(x) is continuous on R and such that
>
> k(x) = (x^2 - 9)/(x - 3)
>
> for x != 3. Must k(3) = 6?
>
> The answer is yes.
>
> But the question didn't _define_ k(x). Rather, it specified
> some conditions on k(x) and then asked a question regarding
> such a function k.
>
> quasi
>


I could include a rule in the definition of the function which says
wherever there is a removable discontinuity, remove it. Can you give me
an example where including such a rule would not result in a set of
ordered pairs satisfying the requirements of a continuous function?
That is assuming a function defined identically with the exception of
that rule results in a function with no more than a finite number of
removable discontinuities and not irremovable discontinuities?


For example, let f(x) = (x^2 - 9)/(x - 3) where (x^2 - 9)/(x - 3) is
defined, else f(x) = limit[(s^2 - 9)/(s - 3), s->x].




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.