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.independent

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 13, 2013 3:32 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 10/9/2013 4:49 AM, Peter Percival wrote:
> Hetware wrote:
>> On 10/7/2013 8:39 PM, Peter Percival wrote:
>>> Hetware wrote:
>>>> On 10/7/2013 4:56 AM, David Bernier wrote:
>>>>> On 10/07/2013 03:21 AM, Robin Chapman wrote:
>>>>>> On 07/10/2013 04:34, Hetware wrote:
>>>>>>> On 9/30/2013 4:03 AM, Robin Chapman wrote:
>>>>>>
>>>>>>>> Hetware: 0/0 = 3
>>>>>>>>
>>>>>>>> Ciekaw: 0/0 = 1
>>>>>>>>
>>>>>>>> Any more entrants?
>>>>>>>>

>>>>>>>
>>>>>>> To be correct; Hetware: 0/0 = 1 (under certain circumstances).

>>>>>>
>>>>>> Not according to your original posting in this thread :-(

>>>>>
>>>>> Heware, if 0/0 = 1, then 0/0 = (100*0)/0 = 100*(0/0) = 100*1 = 100.
>>>>>
>>>>> So, assuming 0/0 = 1, we find that 1 = 100 :(
>>>>>
>>>>> David
>>>>>

>>>>
>>>> That statement came with a qualification. That is, given a function
>>>> defined by f(t) = (t^2-9)/(t-3), I could assume (t-3)/(t-3) = 1, even
>>>> where t=3.

>>>
>>> "given a function defined by" is irrelevant. At t=3 (t-3)/(t-3) is
>>> undefined.
>>>

>>>> I've already shown that a modified version of that
>>>> proposition does make sense.

>>>
>>> No you haven't.
>>>

>>>> Given a function f(t) continuous for all real numbers t and defined by
>>>> (t^2-9)/(t-3) everywhere the expression is meaningful, that function is
>>>> identical to g(t) = (t+3). My original mistake was to assume
>>>> continuity
>>>> after using (t^2-9)/(t-3) to define the entire function.

>>>
>>> What you wish to say is that the function g:R->R defined by
>>>
>>> g(t) = f(t) if t=/=3
>>> = 6 otherwise
>>>
>>> has these properties:
>>> i) g = f where f is defined,
>>> ii) g is defined on the whole of R,
>>> iii) g is continuous.
>>>
>>>
>>>

>>
>> The value of 6 at t=3 follows from the stipulation of continuity.

>
> The value of what? f or g? f has no value at 3.
>


Given a function f(t) continuous for all real numbers t and defined by
(t^2-9)/(t-3) everywhere the expression is meaningful, that function is
identical to g(t) = (t+3).

>> It is
>> meaningful to say that f(t) is continuous over the domain of real
>> numbers.

>
> So what? Is it true? Yes, by proof, not by stipulation.


You cannot prove a definition.

>> It is also meaningful to say that f(t) = (t^2-9)/(t-3)
>> everywhere that the rhs is meaningful.

>
> I would say "f is defined everywhere (in R) that (t^2-9)/(t-3) is defined".


And you would not be giving the same definition as I am giving.

>> That is sufficient information
>> to determine that f(3) = 6.

>
> f(3) doesn't equal anything. One may "fill the gap" by defining g as I
> have done above, *then* g(3) = 6. But g isn't f.
>


"Definition 2-1.1. A function f is a set of ordered pairs, no two of
which have the same first element. The set of first elements of the
pairs is called the domain of the function, whereas the set of second
elements of the pairs is called the range. The domain and range
elements are related by a given rule"

The definition of continuity provides the rule for determining the value
of the function f(3) which is *DEFINED* as continuous, and is given by
f(t) = (t^2-9)/(t-3) where t!=3. By definition f(3) has a definite,
finite value at f(3) and that value is f(3) = limit[(t^2-9)/(t-3), t->3].

Where do you get the idea that one cannot define a function as
continuous? How would you prove, for example, the mean value theorem,
if you could not define an arbitrary function to be continuous?


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.