Search All of the Math Forum:

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

Topic: There are no axioms or postulates in Greek mathematics, only in mythmatics.
Replies: 1   Last Post: Sep 27, 2017 5:03 PM

 Karl-Olav Nyberg Posts: 1,517 Registered: 12/6/04
Re: There are no axioms or postulates in Greek mathematics, only in mythmatics.
Posted: Sep 27, 2017 5:03 PM

onsdag 27. september 2017 22.43.10 UTC+2 skrev John Gabriel følgende:
> On Wednesday, 27 September 2017 12:55:42 UTC-4, konyberg wrote:
> > onsdag 27. september 2017 18.05.46 UTC+2 skrev konyberg følgende:
> > > onsdag 27. september 2017 14.20.13 UTC+2 skrev John Gabriel følgende:
> > > > On Monday, 25 September 2017 19:22:51 UTC-4, John Gabriel wrote:
> > > > > https://www.linkedin.com/pulse/part-1-axioms-postulates-mathematics-john-gabriel
> > > > >
> > > > > https://www.linkedin.com/pulse/part-2-axioms-postulates-mathematics-john-gabriel
> > > > >
> > > > > https://www.linkedin.com/pulse/part-3-axioms-postulates-mathematics-john-gabriel
> > > > >
> > > > > https://www.linkedin.com/pulse/part-4-axioms-postulates-mathematics-john-gabriel
> > > > >
> > > > > https://www.linkedin.com/pulse/part-5-axioms-postulates-mathematics-john-gabriel
> > > > >
> > > > > Comments are unwelcome and will be ignored.
> > > > >
> > > > > Posted on this newsgroup in the interests of public education and to eradicate ignorance and stupidity from mainstream mythmatics.
> > > > >
> > > > > gilstrang@gmail.com (MIT)
> > > > > huizenga@psu.edu (HARVARD)
> > > > > andersk@mit.edu (MIT)
> > > > > david.ullrich@math.okstate.edu (David Ullrich)
> > > > > djoyce@clarku.edu
> > > > > markcc@gmail.com

> > > >
> > > > Here is a quote from the only mainstream academic I respect on sci.math:
> > > >
> > > >
> > > > Euler's teacher was Johann Bernoulli, the more conceited and less genial of the Bernoulli brothers (of course being "less genial" than Jakob B does not mean a reproach). Euler was even more genial than both and many others. Nevetheless here he applied the wrong concept.
> > > >
> > > > John Gabriel is completely correct when he says:
> > > >
> > > > 1. S = Lim S, is wrong

> > > Of course it is wrong! Euler never wrote that!
> > > > 2. The series is not the limit.
> > > Of course not if a series is defined as finite. But if the series is defined as the infinite sum, then it is the limit.
> > > > 3. 1/3 cannot be expressed in base 10 because 3 is not a prime factor of 10.
> > > This, and both 1. and 2. is your own invention. Who is the good professor It is WM!
> > >
> > > KON

> > > >
> > > > Unfortunately the contrary belief has lead to the mess of transfinite set theory.
> > > >
> > > > Regards, WM

> >
> > Ok. Some questions for you, JG.
> > S(n) = (i=0 to n)Sum ((-1)^i a^i)), |a| < 1
> > What is this?
> > Can you give me the closed form?
> >
> > And where do this lead to?
> > S = (n=0 to inf)Sum ((-1)^n a^n)), |a| <1
> > Can you give me the closed form of this?
> >
> > Is it the same as the former?
> >
> > Is it: S(n) = S, or lim S(n) = S, or S(n) = lim S(n), or S = lim S. What do you go for, and what would Euler go for?
> >
> > KON

>
> It does not matter how you choose to represent it. The fact is that Euler defined S = Lim S.
>
> S = 1 - a + a^2 - ...
>
> Lim S = Lim_{n \to \infty} (1-(-a)^n) / (1 + a) = 1 / (1 + a)
>
> S = Lim S

You can not say:
S = ( )
Lim S = Lim ( )
S = Lim S

This is so not a mathematical construction. It is (pardon) just idiotic.

KON