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Topic: 2.01 - In words and pictures: The mainstream definition of limit
fails when f is a constant function.

Replies: 19   Last Post: Jul 13, 2014 12:36 PM

 Messages: [ Previous | Next ]
 johngabriel2009@gmail.com Posts: 354 Registered: 5/25/14
Re: 2.01 - In words and pictures: The mainstream definition of limit
fails when f is a constant function.

Posted: Jul 11, 2014 2:14 AM

On Friday, July 11, 2014 12:59:55 AM UTC+2, dull...@sprynet.com wrote:
> On Thu, 10 Jul 2014 10:43:09 -0700 (PDT), John Gabriel
>
> <johngabriel2009@gmail.com> wrote:
>
>
>

> >On Thursday, July 10, 2014 7:27:51 PM UTC+2, dull...@sprynet.com wrote:
>
> >> On Thu, 10 Jul 2014 04:30:42 -0700 (PDT), John Gabriel
>
> >
>
> >> >http://tutorial.math.lamar.edu/Classes/CalcI/DefnOfLimit.aspx
>
> >
>
> >> >States the definition of limit as follows:
>
> >
>
> >> >Lim (x->c) f(x) = L
>
> >
>
> >> >If for every eps > 0, there is some number delta > 0
>
> >> >SUCH THAT
>
> >> > |f(x)-L| < eps WHENEVER 0 < |x-c| < delta
>
> >> >Suppose f(x)=1.
>
> >> >Then,
>
> >
>
> >> >Lim (x->1) f(x) = 1
>
> >
>
> >> >If for every eps > 0, there is some number delta > 0
>
> >> >SUCH THAT
>
> >> > 0 < eps WHENEVER 0 < |x-c| < delta
>
> >
>
> >> >Analysis:
>
> >
>
> >> >1. There are an innumerable number of deltas greater than 0.
>
> >> >2. 0 < eps WHETHER OR NOT 0 < |x-c| < delta is TRUE or FALSE.
>
> >
>
> >> >eps does not give a shit about delta in this case, and delta equal to ANYTHING, does NOT imply eps > 0.
>
> >
>
> >> True. Totally irrelevant.
>
> >
>
> >Huh?! Irrelevant?! Nein, nein, nein! The whole discussion with Frenchie over here is over "=>"
>
> >
>
> >It is very relevant.
>
> >
>
> >> >delta can be LESS than |x-c| and still eps will be greater than 0.
>
> >> >delta can be GREATER than |x-c| and still eps will be greater than 0.
>
> >> >delta can EVEN be ZERO (except the definition does not allow this) and still eps will be greater than 0.
>
> >
>
> >> True.
>
> >
>
> >Of course it's true.
>
> >
>
> >> >This simple logic is comprehended by high school children, but the morons on this forum can't get it!
>
> >
>
> >> No, the person who doesn't understand the simply logic is you. Those comments about how delta can be anything are correct.
>
> >
>
> >Huh? Not arguing about how delta can be anything. I said this very thing myself.
>
> >
>
> >> It's true that for this function |f(x) - L| < eps no matter
>
> >> what. That's precisely why it's true whenever 0 < |x-c| < delta.
>
> >
>
> >NO!!!!!! The whenever part is WRONG. It has nothing to do with *whenever*. I understand that whenever is part of the definition, I am not rejecting this. BUT, it is NOT TRUE in this case. The fact that "|f(x) - L| < eps no matter what" has nada to do with *whenever*.
>
> >
>
> >
>
> >> See "A happens whenever B happens" does not mean that the times when the two happen are the same. At last that's not what it means in mathematics.
>
> >
>
> >But it DOES MEAN that B happens as a result of A.
>
>
>
>
>
> No. Absolitely positively not. "B happens as a resut of A"
>
> is one hundred percent what it does not mean.

Absolutely 100% that's exactly what it means.

>
>
> You really should learn some of this stuff.

> Your errors are not original, they're mostly the
>
> typical errors that students make when they
>
> start to study this stuff.

In this case, it's YOU who are making errors, NOT your students. They are thinnking correctly!

>
>
>

> > As I have been telling Frenchie (and you now!), that is simply UNTRUE. In this comment you have agreed with me even though you don't realise it! Chuckle.
>
> >
>
> >> You seem to think that the statement
>
> >> (*) 2+2=4 whenever x > 5
>
> >> is false.
>
> >
>
> >It is VERY FALSE. 2+2=4 even if x = SHIT. Chuckle.
>
> >
>
> >> In fact (*) is true.
>
> >
>
> >Nonsense.
>
> >
>
> >> Of course it's a very curious thing to say, but that doesn't make it false.
>
> >
>
> >Indeed. It's bullshit.
>
> >
>
> >> 2+2 is _always_ equal to 4. And since it's always equal to 4, in particular it is equal to 4 whenever x > 5.
>
> >
>
> >Horse-feathers and you know it dullrich!!!! Here you are lecturing me about 'academic' integrity and lies. Hypocrite.
>
> >
>
> >> You really do need to get these simple matters of logic and terminology straight before trying to "refute" things.
>
> >
>
> >Chuckle!
>
> >
>
> >Read as: You really do need to use our terminology and accept our understanding flawed or not.
>
> >
>
> >Sorry dullrich. No can do.
>
> >
>
> >> Otherwiise you make a fool of yourself.
>
> >
>
> >On the contrary, it is you and Frenchie who are making fools of yourselves.
>
> >
>
> >> >For a rigorous definition that works for ALL functions, see Gabriel's New Limit theorem (read about it the NEWS section at my website: http://thenewcalculus.weebly.com). By the way, the New Calculus does not use ill-formed limits, infinity or infinitesimals.
>
> >
>
> >> >Comments are NOT welcome. This comment is produced in the interests of public education; and to eradicate ignorance and stupidity in mainstream mythmatics.
>
>
>
> "Let's just say that even if you were correct (not a chance in hell!),
>
> I would find a way to confound you." - John Gabriel admits that
>
> "winning" is more important than mathematical correctness.
>
>
>
> David C. Ullrich