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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 20, 2013 12:43 PM
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On 10/19/2013 11:30 PM, Arturo Magidin wrote:
> On Saturday, October 19, 2013 7:42:48 PM UTC-5, Hetware wrote:

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

Are those your parents?

You are wrong to think that I am somehow emotionally attached to being
right in my original assertions. As I have already stated, I do not
conform my understanding to the assertions of others unless I understand
and can validate those assertions.

If I fully understood the subtleties involved, I would not be spending
nearly as much time discussing this matter. I am seeking understanding,
not vindication.

>> What convention is that?
>
> As I explained eariler:
>
> The convention that when the domain of a function is not explicitly
> stated, then the domain is taken to be the "natural domain" of the
> function.
>
> The "natural domain" of a function that is given via a formula *and
> no other specification* is taken to be the set of all real numbers
> for which the formula, as given, makes sense and yields a real
> number.


Given some real-valued function of real-valued arguments, defined
everywhere on R, is it true that the function is either continuous, or
not continuous?

Let P(f) be the proposition that f(x) is continuous for all x in R.
Then !P(f) means f(x) is discontinuous for some x in R.

Does P(f) have meaning? Is it an admissible mathematical statement?

> You keep talking about assumptions of continuity, assumptions of
> this, assumptions of that, authors trying to "bait" you, etc. But you
> keep ignoring the conventions.
>

>>> 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.

>
> And so we get back to your self-justifying dance. Sorry, I don't
> tango with the willfully ignorant.
>


Let P(f) <=> f(x) is continuous for all x in R.
Let D(f) <=> f(x) has a finite value for all x in R.
Let L(f) <=> limit[f(s), s->x] exists for all x in R.
Let Q(f) <=> f(x) = limit[f(s), s->x]

P <=> D & L & Q
Q => D

Let f(x) be in R for all x in R other than x=0, f(0) = 0/0 and
limit[f(s), s->x] exist for all x in R.

D(f) => F
L(f) => T
Q(f) => F
!P(f) <= F & T & F

Let g(x) be a continuous function on R such that g(x) = f(x) when f(x)
is a real number.

D(g) => T
L(g) => T
Q(g) => T
P(g) <= T & T & T

So Quasi was correct. I can define a function g(x) to be continuous,
but it is not the same function as the function f(x) used to define g(x)
everywhere f(x) is defined.


Date Subject Author
9/28/13
Read Is (t^2-9)/(t-3) defined at t=3?
Hetware
9/28/13
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Michael F. Stemper
9/28/13
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quasi
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Hetware
9/28/13
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quasi
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Peter Percival
9/29/13
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quasi
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Hetware
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Richard Tobin
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Hetware
9/28/13
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Hetware
10/6/13
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Hetware
10/6/13
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Hetware
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Hetware
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fom
10/13/13
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fom
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fom
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9/30/13
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