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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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Hetware

Posts: 148
Registered: 4/13/13
Re: Is (t^2-9)/(t-3) defined at t=3?
Posted: Oct 8, 2013 7:55 PM
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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.


Date Subject Author
9/28/13
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Hetware
9/28/13
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Michael F. Stemper
9/28/13
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scattered
9/28/13
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Hetware
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quasi
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Hetware
9/28/13
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quasi
9/28/13
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Peter Percival
9/29/13
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quasi
9/28/13
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Hetware
9/28/13
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Richard Tobin
9/28/13
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Hetware
9/28/13
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tommyrjensen@gmail.com
9/29/13
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Hetware
10/6/13
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Hetware
10/6/13
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Peter Percival
10/6/13
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Hetware
10/6/13
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quasi
10/8/13
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quasi
10/7/13
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Peter Percival
9/29/13
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Michael F. Stemper
9/29/13
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Hetware
9/29/13
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quasi
9/29/13
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Hetware
9/29/13
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magidin@math.berkeley.edu
10/6/13
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Hetware
10/6/13
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magidin@math.berkeley.edu
10/7/13
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Hetware
10/7/13
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LudovicoVan
10/7/13
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Peter Percival
10/8/13
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magidin@math.berkeley.edu
10/12/13
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Hetware
10/12/13
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fom
10/13/13
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magidin@math.berkeley.edu
10/13/13
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Richard Tobin
10/13/13
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Hetware
10/13/13
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Peter Percival
10/13/13
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fom
10/13/13
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magidin@math.berkeley.edu
10/13/13
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magidin@math.berkeley.edu
10/8/13
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quasi
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magidin@math.berkeley.edu
10/8/13
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quasi
10/8/13
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10/12/13
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Hetware
10/13/13
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quasi
10/13/13
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Peter Percival
10/9/13
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magidin@math.berkeley.edu
10/9/13
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fom
10/10/13
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magidin@math.berkeley.edu
10/10/13
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fom
10/7/13
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Peter Percival
10/7/13
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Hetware
10/7/13
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fom
10/7/13
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Peter Percival
9/29/13
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quasi
9/30/13
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Peter Percival
9/30/13
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Peter Percival
9/30/13
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Peter Percival
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9/28/13
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Hetware
9/29/13
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9/28/13
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Virgil
9/29/13
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Virgil
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Hetware
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Virgil
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9/30/13
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10/6/13
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Hetware
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Peter Percival
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Peter Percival
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David Bernier
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Hetware
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Ciekaw
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10/8/13
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Hetware
10/9/13
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Peter Percival
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Virgil
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Hetware
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10/9/13
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10/10/13
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Ciekaw
10/9/13
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10/10/13
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10/13/13
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10/13/13
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10/13/13
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Hetware
10/14/13
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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
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Hetware
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fom
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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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10/20/13
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Hetware
10/20/13
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10/20/13
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10/20/13
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Hetware
10/20/13
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10/20/13
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Hetware
10/20/13
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10/19/13
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fom

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