Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

Topic: Is (t^2-9)/(t-3) defined at t=3?
Replies: 166   Last Post: Oct 30, 2013 9:41 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   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
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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
rules lead collectively to a contradiction, then our definition must be
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
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
Read Re: Is (t^2-9)/(t-3) defined at t=3?
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
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Peter Percival
10/8/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
magidin@math.berkeley.edu
10/12/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
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
Read Re: Is (t^2-9)/(t-3) defined at t=3?
quasi
10/12/13
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?
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
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
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
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
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?
RGVickson@shaw.ca
9/30/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Roland Franzius
9/30/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Richard Tobin
9/30/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
RGVickson@shaw.ca
9/28/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Peter Percival
9/28/13
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?
Peter Percival
9/28/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Virgil
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?
Virgil
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?
LudovicoVan
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?
Virgil
9/29/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
magidin@math.berkeley.edu
9/29/13
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?
FredJeffries@gmail.com
9/30/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Hetware
9/30/13
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?
Peter Percival
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?
magidin@math.berkeley.edu
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?
magidin@math.berkeley.edu
10/6/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
David Bernier
9/29/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Peter Percival
9/28/13
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?
Richard Tobin
9/30/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Ciekaw
9/30/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Robin Chapman
9/30/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Virgil
9/30/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
LudovicoVan
9/30/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
LudovicoVan
10/6/13
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?
Robin Chapman
10/7/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
David Bernier
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
10/8/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Hetware
10/9/13
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?
Richard Tobin
10/7/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Peter Percival
10/8/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Hetware
10/8/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Virgil
10/8/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Hetware
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?
Peter Percival
10/10/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Ciekaw
10/9/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Peter Percival
10/10/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Tim Golden BandTech.com
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?
Hetware
10/14/13
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?
Hetware
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?
Hetware
10/13/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
fom
10/14/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
fom
10/14/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Hetware
10/14/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
magidin@math.berkeley.edu
10/14/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
magidin@math.berkeley.edu
10/14/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Peter Percival
10/14/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Hetware
10/14/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
quasi
10/16/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
@less@ndro
10/16/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
quasi
10/19/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Hetware
10/19/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
quasi
10/19/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Hetware
10/20/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
fom
10/20/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
quasi
10/20/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Hetware
10/20/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
fom
10/20/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Hetware
10/20/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Peter Percival
10/20/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Richard Tobin
10/20/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Hetware
10/30/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
@less@ndro
10/19/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Hetware
10/10/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Ronald Benedik
10/10/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Peter Percival
10/10/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Virgil
10/18/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Hetware
10/19/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Peter Percival
10/19/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
fom
10/19/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Peter Percival
10/19/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Hetware
10/19/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Peter Percival
10/19/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Hetware
10/19/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
fom
10/19/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
magidin@math.berkeley.edu
10/19/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Hetware
10/19/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
magidin@math.berkeley.edu
10/20/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Hetware
10/20/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
quasi
10/20/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
quasi
10/20/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Hetware
10/20/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Peter Percival
10/20/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
magidin@math.berkeley.edu
10/20/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Hetware
10/20/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Arturo Magidin
10/20/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
Hetware
10/20/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
magidin@math.berkeley.edu
10/19/13
Read Re: Is (t^2-9)/(t-3) defined at t=3?
fom

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.