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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 ]
 Hetware Posts: 148 Registered: 4/13/13
Re: Is (t^2-9)/(t-3) defined at t=3?
Posted: Oct 19, 2013 8:42 PM

On 10/19/2013 6:21 PM, Arturo Magidin wrote:
> On Saturday, October 19, 2013 12:55:37 PM UTC-5, Hetware wrote:
>> On 10/19/2013 7:34 AM, Peter Percival wrote:
>>

>>> Hetware wrote:
>>
>>>
>>
>>>> If we define f(x) as
>>
>>>>
>>
>>>> f(x) = x/x and c[f(x)],
>>
>>>
>>
>>> That's cheating. You've been told at least eight million times
>>
>>
>>
>> In psychology that's called cognitive distortion, and is an example
>> of
>>
>> how emotions cause our thoughts to be irrational.

>
> Hey, Mr. Pot. Have you met Ms Kettle?
>

>>> that you
>>
>>> may define f with a formula, but you cannot put "and c[f(x)]" in
>>> the

>>
>>> definition. If c[f(x)] is true it has to be proved _from_ the
>>> definition.

>>
>>
>>
>> Sayin' it don't make it so.

>
>
> Apparently no, you have not met Ms Kettle.
>
> You made a mistake because you purposely chose to disregard the
> convention that the author set forth.

What convention is that?

> Rather than admit this, you are going out of your way to try to prove
> that you were right all along.

The proposition P(f) that "f(x) is continuous" appears to have meaning.
So either P or !P.

P implies that f(x) is defined everywhere on the proposed domain. It
also implies that over the proposed domain limit[f(s), s->x] exists, is
finite, and f(x) = limit[f(s), s->x].

It is common to define a function using multiple rules. For example
s(x) = sqrt(x^2) for x >= 0 and s(x) = -sqrt(x^2) otherwise. That is,
we state a rule and the condition under which the rule applies. If our
abandoned. It is possible to have two rules with overlapping
conditions. For example, s(x) = sqrt(x^2) for x >= 0 and s(x) =
-sqrt(x^2) for x <= 0; The condition for both rules is satisfied when x
= 0. This is not a problem since both rules produce the same value.

It is possible to define a piecewise function such that p(x) = v(x)
where v(x) does not produce an indeterminate form and p(x) = L(x)
everywhere.

Given a mapping f(x) for which the limit[f(s), s->x] exists and is
finite over the proposed domain, the proposition P(f) implies that f(x)
= limit[f(s), s->x] over the proposed domain. So P(f) is true.

!P(f) implies that for some x either f(x) is undefined, lacks a finite
limit, or f(x) != limit[f(s), s->x]. These rules do not permit us to
use f(x) = limit[f(s), s->x] to determine the value of f(x) because we
nothing implies the rule to be true. If f(x) results in an
indeterminate form, we have not recourse to the implications P, and we
therefore conclude !P(f) is true.

So P(f) = !P(f).

> Well on your way to becoming a crank, despite whatever intelligence
> or competence you may have. Congratulations. You are fighting hard to
> stay ignorant.
>

http://mitpress2.mit.edu/catalog/item/default.asp?ttype=2&tid=9431

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