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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

 Messages: [ Previous | Next ]
 Virgil Posts: 8,833 Registered: 1/6/11
Re: Is (t^2-9)/(t-3) defined at t=3?
Posted: Oct 8, 2013 8:00 PM

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!
--

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