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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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magidin@math.berkeley.edu

Posts: 11,117
Registered: 12/4/04
Re: Is (t^2-9)/(t-3) defined at t=3?
Posted: Oct 9, 2013 1:35 AM
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On Tuesday, October 8, 2013 8:46:32 PM UTC-5, Hetware wrote:
> On 10/8/2013 8:00 PM, Virgil wrote:
>

> > In article <YN6dnYEy-eEPBsnPnZ2dnUVZ_sqdnZ2d@megapath.net>,
>
> > Hetware <hattons@speakyeasy.net> 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. It is
>
> >> meaningful to say that f(t) is continuous over the domain of real
>
> >> numbers. It is also meaningful to say that f(t) = (t^2-9)/(t-3)
>
> >> everywhere that the rhs is meaningful. That is sufficient information
>
> >> to determine that f(3) = 6.
>
> >
>
> > It is not, however, meaningful to define a function by
>
> > f(t) = (t^2-9)/(t-3) and then expect it to be either defined
>
> > or continuous at x = 3.
>
> >
>
> > Which you did!
>
> >
>
>
>
> Originally, I did that. I was attempting to understand why it seemed
>
> possible to simply assume the function to be continuous at t=3, and then
>
> treat it as f(t) = (t^2-9)/(t-3) = t+3. The problem was that I was
>
> assuming more about the function than is given by the definition f(t) =
>
> (t^2-9)/(t-3).


Which is, pretty much, what everyone was telling and you were ignoring.

--
Arturo Magidin


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
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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
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Peter Percival
10/8/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
magidin@math.berkeley.edu
10/12/13
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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
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quasi
10/12/13
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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
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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
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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
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RGVickson@shaw.ca
9/30/13
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Roland Franzius
9/30/13
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Richard Tobin
9/30/13
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RGVickson@shaw.ca
9/28/13
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Peter Percival
9/28/13
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Hetware
9/29/13
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Peter Percival
9/28/13
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Virgil
9/29/13
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quasi
9/29/13
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Virgil
9/29/13
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Hetware
9/29/13
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quasi
9/29/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Hetware
9/29/13
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LudovicoVan
9/29/13
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quasi
9/29/13
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Virgil
9/29/13
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magidin@math.berkeley.edu
9/29/13
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Peter Percival
9/29/13
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FredJeffries@gmail.com
9/30/13
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Hetware
9/30/13
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magidin@math.berkeley.edu
10/6/13
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Hetware
10/6/13
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Peter Percival
10/6/13
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Peter Percival
10/6/13
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magidin@math.berkeley.edu
10/6/13
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Peter Percival
10/6/13
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magidin@math.berkeley.edu
10/6/13
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David Bernier
9/29/13
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Peter Percival
9/28/13
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Hetware
9/29/13
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Richard Tobin
9/30/13
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Ciekaw
9/30/13
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Robin Chapman
9/30/13
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Virgil
9/30/13
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LudovicoVan
9/30/13
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LudovicoVan
10/6/13
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Hetware
10/7/13
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Robin Chapman
10/7/13
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David Bernier
10/7/13
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Hetware
10/7/13
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LudovicoVan
10/8/13
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Hetware
10/9/13
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Peter Percival
10/9/13
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Richard Tobin
10/7/13
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Peter Percival
10/8/13
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Hetware
10/8/13
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Virgil
10/8/13
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Hetware
10/9/13
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magidin@math.berkeley.edu
10/9/13
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Peter Percival
10/10/13
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Ciekaw
10/9/13
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Peter Percival
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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Peter Percival
10/13/13
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Hetware
10/14/13
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Peter Percival
10/13/13
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Hetware
10/13/13
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fom
10/13/13
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Hetware
10/13/13
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fom
10/14/13
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fom
10/14/13
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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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@less@ndro
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
10/20/13
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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
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10/20/13
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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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10/20/13
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10/19/13
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fom

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