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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: Sep 30, 2013 8:20 PM
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On 9/29/2013 6:29 PM, FredJeffries wrote:
> On Saturday, September 28, 2013 1:15:47 PM UTC-7, Hetware wrote:
>>
>> So the answer is consensus among mathematicians holds that F(t) = (t^2 -
>> 9)/(t - 3) is undefined at t=3? Perhaps what I should have said at the
>> outset is something along the lines of: on any given day, if I'm setting
>> up an equation in physics, and produce an expression such as F(t) = (t^2
>> - 9)/(t - 3), I treat it as t+3, and do not expect any adverse
>> consequence from doing so.

>
> But you are not setting up an equation in physics. You are
> attempting to learn calculus.
>


No. I'm reading the chapter for the nth time. I already know calculus.
I am perfectly capable of accepting something as true and follow
arguments based upon that predicate.

> Professor Thomas has a very good reason for showing you this
> trivial-seeming example of a function with what is known
> as a "removable singularity". If you are patient and continue
> to study his book you will find his reasons. Here's a hint:
> the function sin(x)/x has the same feature at x = 0.


I'm not sure how the first prepares me for the second.


>> If I conceive of mathematics as an exercise in defining and manipulating
>> symbols, it seems that declaring constructs such as F(t) = (t^2 - 9)/(t
>> - 3) to be undefined at t=3 is arbitrary. The fact that there is an
>> obvious candidate for a value of F(t) at t=3 tells me that accepting
>> that candidate as the value at t=3 does not contradict the definition of
>> a single valued function of one variable.

>
> Of course it does not contradict the definition of a single valued
> function of one variable. It contradicts the definition of one
> particular function, namely Professor Thomas's F(t). The fact that
> this all seems totally arbitrary to you is just because you
> don't know the whole story yet.
>


A function is a mapping from elements of a range to elements of a
domain. Often the image is required to be single valued, but Thomas
does not stipulate that requirement. If I can deterministically
interpret a formal expression as such a mapping, then my interpretation
of that formal expression satisfies the definition of a function.


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
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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
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Peter Percival
9/29/13
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Michael F. Stemper
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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
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Peter Percival
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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
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10/13/13
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fom
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magidin@math.berkeley.edu
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quasi
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fom
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fom
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Hetware
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fom
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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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Hetware
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Virgil
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Virgil
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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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10/14/13
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fom
10/14/13
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Hetware
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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
10/20/13
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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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magidin@math.berkeley.edu
10/20/13
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Hetware
10/20/13
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quasi
10/20/13
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Hetware
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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10/20/13
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10/19/13
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