
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 < xc < 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 < xc < delta > > > > > >> >Analysis: > > > > > >> >1. There are an innumerable number of deltas greater than 0. > > >> >2. 0 < eps WHETHER OR NOT 0 < xc < 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 xc and still eps will be greater than 0. > > >> >delta can be GREATER than xc 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 < xc < 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.
Listen idiot, follow your advice!
> 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. > > > > > >Horsefeathers 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 illformed 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

