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Topic: John Gabriel's Thread on Mathematics.
Replies: 231   Last Post: Mar 22, 2014 9:23 PM

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Karl-Olav Nyberg

Posts: 1,541
Registered: 12/6/04
Re: New Calculus for Dummies.
Posted: Mar 1, 2014 9:35 PM
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On Saturday, March 1, 2014 8:08:21 PM UTC+1, John Gabriel wrote:
> On Saturday, 1 March 2014 19:20:50 UTC+2, dull...@sprynet.com wrote:
>

> > I asked how you find the derivative of sin(x). You showed me a proof
>
>
>
>
>

> > I asked how you find the derivative of sin(x). You showed me a proof
>
> using the power series.
>
>
>
> The power series was only used in the last couple of steps to show you that the numerator is indeed divisible by m+n. Using the power series DOES NOT contradict anything I have said. It does not invalidate anyone of my claims.
>
>
>

> > Now when I ask the obvious questions about that you say you didn't have to.
>
>
>
> I gave you valid reasons. Here is how arc length was derived without calculus:
>
>
>
> https://www.filesanywhere.com/fs/v.aspx?v=8b6c688d5b6375ac73a3
>
>
>
> This means I am allowed to use power series.
>
>
>
> And if you think that I need the Taylor series, think again! Here is the Gabriel polynomial:
>
>
>
> https://www.filesanywhere.com/fs/v.aspx?v=8b6c688d5b63747d6b9b
>
>
>
> It is more rigorous than the Taylor series.
>
>
>

> >You should either answer my questions or _show_ me the proof without power series.
>
>
>
> As I said, I am allowed to use power series because it's not infinite. There is no such thing as an "infinite" series. There is no "infinite" ANYTHING! :-)
>
>
>

> > >> See, I thought the point was the New Calculus was going to avoid
>
> > >> limits.
>
>
>
> It does. :-)
>
>
>

> >How in the world do you make sense of a power series without limits.
>
>
>
> It's an approximation series which is identified by the fact of convergence. So, although it has a limit, the limit is not used, because in most cases, we don't know what it is! :-)
>
>
>

> > Not infinite except for being an infinite series, fine.
>
>
>
> The ellipsis, that is, ... does not make anything infinite.
>
>
>
> sin(x) =/= x - x^3/3! + x^5/5! ...
>
>
>
> sin(x) = LIMIT (x - x^3/3! + x^5/5! ... )
>
>
>
> Big difference.
>
>
>
>
>

> > Also the proof that you have the fiirst three terms right. As well
>
> > as an expllanation of what you mean by that...
>
>
>
> We can tell by a only a few successive terms whether a series converges or not. We do not even need to know if it has a limit! :-) In most cases, that's how we show a series converges, that is, by investigating the given terms. I think a better than for sin(x) = x - x^3/3! + x^5/5! ... is "partial series" or "incomplete series". The word infinite is a misnomer.
>
>
>

> >Huh? Then show me the proof that just uses the first three terms.
>
> Also the proof that you have the fiirst three terms right. As well
>
> as an expllanation of what you mean by that...
>
>
>
> I am not sure what you mean here. Sine is an approximation in most cases.
>
>
>
> You can study the Gabriel Polynomial mentioned earlier. It contains ZERO limits.
>
>
>

> > What's the diifference?
>
>
>
> Huge. 1 is a number but sin(x) is not a number, in most cases it is an incommensurable magnitude that can only be approximated by a rational number.


Hi.

I think there is some confusion here.
JG doesn't use a Taylor series to prove his point, but a Taylor polynom. But of course we don't prove anything by using Taylor polynomes (We use it to approximate.). He thinks he actually can use polynomes to prove things. It's like giving examples in mathematics that this fits (aritmically), and then conclude that this is generally proved.

KON


Date Subject Author
2/22/14
Read John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/23/14
Read Re: John Gabriel's Thread on Mathematics.
Brian Q. Hutchings
2/23/14
Read Re: John Gabriel's Thread on Mathematics.
Brian Q. Hutchings
2/23/14
Read Re: John Gabriel's Thread on Mathematics.
Wizard-Of-Oz
2/23/14
Read Re: John Gabriel's Thread on Mathematics.
Wizard-Of-Oz
2/23/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/23/14
Read Re: John Gabriel's Thread on Mathematics.
Wizard-Of-Oz
2/23/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/23/14
Read Re: John Gabriel's Thread on Mathematics.
Wizard-Of-Oz
2/23/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/23/14
Read Re: John Gabriel's Thread on Mathematics.
Wizard-Of-Oz
2/23/14
Read Re: John Gabriel's Thread on Mathematics.
Dirk Van de moortel
2/23/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/23/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/23/14
Read Re: John Gabriel's Thread on Mathematics.
Wizard-Of-Oz
2/23/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/23/14
Read Re: John Gabriel's Thread on Mathematics.
Wizard-Of-Oz
2/23/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/24/14
Read Re: John Gabriel's Thread on Mathematics.
Wizard-Of-Oz
2/24/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/24/14
Read Re: John Gabriel's Thread on Mathematics.
Wizard-Of-Oz
2/24/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/24/14
Read Re: John Gabriel's Thread on Mathematics.
Wizard-Of-Oz
2/24/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/24/14
Read Re: John Gabriel's Thread on Mathematics.
Wizard-Of-Oz
2/24/14
Read Re: John Gabriel's Thread on Mathematics.
Brian Q. Hutchings
2/24/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/24/14
Read Re: John Gabriel's Thread on Mathematics.
Wizard-Of-Oz
2/25/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/25/14
Read Re: John Gabriel's Thread on Mathematics.
Wizard-Of-Oz
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
Wizard-Of-Oz
2/24/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/24/14
Read Re: John Gabriel's Thread on Mathematics.
Brian Q. Hutchings
2/23/14
Read Re: John Gabriel's Thread on Mathematics.
Art Hopkins
2/23/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/23/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/23/14
Read Re: John Gabriel's Thread on Mathematics.
Dirk Van de moortel
2/23/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/23/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/23/14
Read Space time and the universe (STATU).
thenewcalculus@gmail.com
2/24/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/24/14
Read Re: John Gabriel's Thread on Mathematics.
Wizard-Of-Oz
2/24/14
Read Re: John Gabriel's Thread on Mathematics.
Giddy Armstrong
2/24/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/24/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
Wizard-Of-Oz
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
Wizard-Of-Oz
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
YBM
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
Wizard-Of-Oz
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
Wizard-Of-Oz
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
Roland Franzius
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
Wizard-Of-Oz
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
Wizard-Of-Oz
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
Wizard-Of-Oz
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
Inverse 18 Mathematics
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
Inverse 18 Mathematics
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
Karl-Olav Nyberg
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
Karl-Olav Nyberg
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
Wizard-Of-Oz
2/26/14
Read the story of number (what is the canonical representation of
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Brian Q. Hutchings
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
Brian Q. Hutchings
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
Wizard-Of-Oz
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
Wizard-Of-Oz
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/26/14
Read New Calculus for Dummies.
thenewcalculus@gmail.com
2/27/14
Read Re: New Calculus for Dummies.
Wizard-Of-Oz
2/27/14
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thenewcalculus@gmail.com
2/27/14
Read Re: New Calculus for Dummies.
David C. Ullrich
2/27/14
Read Re: New Calculus for Dummies.
thenewcalculus@gmail.com
2/28/14
Read Re: New Calculus for Dummies.
David C. Ullrich
2/28/14
Read 'rithmetical (trivial
Brian Q. Hutchings
2/28/14
Read Re: 'rithmetical (trivial
Peter Percival
2/28/14
Read Re: 'rithmetical (trivial
fom
2/28/14
Read 'rithmetical (trivial
Brian Q. Hutchings
2/28/14
Read Re: New Calculus for Dummies.
John Gabriel
3/1/14
Read Re: New Calculus for Dummies.
David C. Ullrich
3/1/14
Read Re: New Calculus for Dummies.
ross.finlayson@gmail.com
3/1/14
Read Re: New Calculus for Dummies.
thenewcalculus@gmail.com
3/1/14
Read Re: New Calculus for Dummies.
thenewcalculus@gmail.com
3/1/14
Read Re: New Calculus for Dummies.
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3/1/14
Read Re: New Calculus for Dummies.
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3/2/14
Read Re: New Calculus for Dummies.
Wizard-Of-Oz
3/2/14
Read Re: New Calculus for Dummies.
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3/2/14
Read Re: New Calculus for Dummies.
thenewcalculus@gmail.com
3/2/14
Read Re: New Calculus for Dummies.
David C. Ullrich
3/2/14
Read Re: New Calculus for Dummies.
John Gabriel
3/3/14
Read Re: New Calculus for Dummies.
John Gabriel
3/3/14
Read Re: New Calculus for Dummies.
David C. Ullrich
3/3/14
Read Re: New Calculus for Dummies.
thenewcalculus@gmail.com
3/4/14
Read Re: New Calculus for Dummies.
David C. Ullrich
3/4/14
Read Re: New Calculus for Dummies.
thenewcalculus@gmail.com
3/4/14
Read Re: New Calculus for Dummies.
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3/4/14
Read Re: New Calculus for Dummies.
thenewcalculus@gmail.com
3/4/14
Read Re: New Calculus for Dummies.
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3/5/14
Read Re: New Calculus for Dummies.
thenewcalculus@gmail.com
3/4/14
Read Re: New Calculus for Dummies.
David C. Ullrich
3/5/14
Read Re: New Calculus for Dummies.
thenewcalculus@gmail.com
3/5/14
Read Re: New Calculus for Dummies.
David C. Ullrich
3/5/14
Read Re: New Calculus for Dummies.
thenewcalculus@gmail.com
3/6/14
Read Re: New Calculus for Dummies.
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3/6/14
Read Re: New Calculus for Dummies.
thenewcalculus@gmail.com
3/6/14
Read "skwaring the cyrcle
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3/3/14
Read Re: New Calculus for Dummies.
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3/3/14
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3/3/14
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3/4/14
Read Re: New Calculus for Dummies.
ross.finlayson@gmail.com
3/3/14
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3/3/14
Read Re: New Calculus for Dummies.
thenewcalculus@gmail.com
3/3/14
Read Re: New Calculus for Dummies.
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3/4/14
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thenewcalculus@gmail.com
3/4/14
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3/8/14
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3/8/14
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3/8/14
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thenewcalculus@gmail.com
3/8/14
Read base-zero for fun (but not infinite series
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3/8/14
Read Re: New Calculus for Dummies.
Peter Percival
3/8/14
Read Re: New Calculus for Dummies.
thenewcalculus@gmail.com
3/9/14
Read Re: New Calculus for Dummies.
Peter Percival
3/9/14
Read Re: New Calculus for Dummies.
thenewcalculus@gmail.com
3/10/14
Read calculi
Brian Q. Hutchings
3/12/14
Read Re: New Calculus for Dummies.
Peter Percival
3/12/14
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thenewcalculus@gmail.com
3/12/14
Read Re: New Calculus for Dummies.
Peter Percival
3/13/14
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thenewcalculus@gmail.com
3/12/14
Read Re: New Calculus for Dummies.
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3/8/14
Read Re: New Calculus for Dummies.
Virgil
3/8/14
Read Re: New Calculus for Dummies.
thenewcalculus@gmail.com
3/9/14
Read Re: New Calculus for Dummies.
Peter Percival
3/9/14
Read Re: New Calculus for Dummies.
thenewcalculus@gmail.com
3/12/14
Read Re: New Calculus for Dummies.
Peter Percival
3/12/14
Read Re: New Calculus for Dummies.
thenewcalculus@gmail.com
3/12/14
Read geometry for ... folks (ratios in constructive [synthetic geometry
Brian Q. Hutchings
3/13/14
Read Re: New Calculus for Dummies.
David C. Ullrich
3/13/14
Read Re: New Calculus for Dummies.
thenewcalculus@gmail.com
3/13/14
Read calculi
Brian Q. Hutchings
3/22/14
Read Re: New Calculus for Dummies.
Al Bundy
3/9/14
Read Re: New Calculus for Dummies.
thenewcalculus@gmail.com
3/1/14
Read Re: New Calculus for Dummies.
Tom Traubert
3/1/14
Read Re: New Calculus for Dummies.
thenewcalculus@gmail.com
2/27/14
Read Re: New Calculus for Dummies.
fom
2/27/14
Read Re: New Calculus for Dummies.
thenewcalculus@gmail.com
2/27/14
Read Re: New Calculus for Dummies.
Ross Donglemeier
2/27/14
Read Re: New Calculus for Dummies.
thenewcalculus@gmail.com
2/27/14
Read Re: New Calculus for Dummies.
PianoMan
2/27/14
Read Re: New Calculus for Dummies.
thenewcalculus@gmail.com
2/28/14
Read Re: New Calculus for Dummies.
Harman Kardan
2/27/14
Read Re: New Calculus for Dummies.
Ross Donglemeier
2/27/14
Read Re: New Calculus for Dummies.
thenewcalculus@gmail.com
2/26/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/27/14
Read What you had to know in mathematics but your educators could not tell you.
thenewcalculus@gmail.com
2/27/14
Read Re: What you had to know in mathematics but your educators could not tell you.
Wizard-Of-Oz
2/27/14
Read Re: What you had to know in mathematics but your educators could not
tell you.
thenewcalculus@gmail.com
2/27/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/27/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/27/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/27/14
Read Re: John Gabriel's Thread on Mathematics.
Wizard-Of-Oz
2/27/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/28/14
Read Re: John Gabriel's Thread on Mathematics.
Wizard-Of-Oz
2/28/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/28/14
Read Re: John Gabriel's Thread on Mathematics.
Wizard-Of-Oz
2/27/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
2/27/14
Read Re: John Gabriel's Thread on Mathematics.
Brian Q. Hutchings
3/1/14
Read Construction of rational numbers and arithmetic axioms.
thenewcalculus@gmail.com
3/1/14
Read Re: Construction of rational numbers and arithmetic axioms.
sceptic
3/1/14
Read Re: Construction of rational numbers and arithmetic axioms.
thenewcalculus@gmail.com
3/1/14
Read Re: Construction of rational numbers and arithmetic axioms.
Wizard-Of-Oz
3/1/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
3/1/14
Read Re: John Gabriel's Thread on Mathematics.
Sal Honda
3/1/14
Read Bourbaki did iT
Brian Q. Hutchings
3/1/14
Read Re: Bourbaki did iT
thenewcalculus@gmail.com
3/1/14
Read The Gabriel Polynomial
thenewcalculus@gmail.com
3/1/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
3/2/14
Read Re: John Gabriel's Thread on Mathematics.
Karl-Olav Nyberg
3/2/14
Read Re: John Gabriel's Thread on Mathematics.
Karl-Olav Nyberg
3/2/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
3/2/14
Read Re: John Gabriel's Thread on Mathematics.
John Gabriel
3/2/14
Read Re: John Gabriel's Thread on Mathematics.
John Gabriel
3/2/14
Read Re: John Gabriel's Thread on Mathematics.
Wizard-Of-Oz
3/2/14
Read Gabriel's Polynomial
thenewcalculus@gmail.com
3/2/14
Read Re: Gabriel's Polynomial - absolutely useless
Wizard-Of-Oz
3/2/14
Read Re: Gabriel's Polynomial - absolutely useless
thenewcalculus@gmail.com
3/2/14
Read The Gabriel Polynomial - One of the many great features in the New Calculus.
thenewcalculus@gmail.com
3/2/14
Read How New Ideas and Knowledge are often treated.
thenewcalculus@gmail.com
3/2/14
Read Re: How New Ideas and Knowledge are often treated.
Wizard-Of-Oz
3/2/14
Read Re: The Gabriel Polynomial - One of the many great features in the New Calculus.
Wizard-Of-Oz
3/2/14
Read Re: Gabriel's Polynomial - absolutely useless
Wizard-Of-Oz
3/3/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
3/4/14
Read Construction of Rational Numbers.
thenewcalculus@gmail.com
3/4/14
Read Re: Construction of Rational Numbers. - still useless
Wizard-Of-Oz
3/4/14
Read Re: Construction of Rational Numbers.
Peter Percival
3/4/14
Read Re: Construction of Rational Numbers.
thenewcalculus@gmail.com
3/4/14
Read Re: Construction of Rational Numbers.
Major Doctor
3/5/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
3/5/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
3/6/14
Read True knowledge or Cantor's Fools Paradise, which?
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3/6/14
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3/6/14
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3/6/14
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3/6/14
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thenewcalculus@gmail.com
3/6/14
Read Re: The first and only rigorous formulation of calculus in human history.
Dirk Van de moortel
3/6/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
3/7/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
3/8/14
Read Re: John Gabriel's Thread on Mathematics.
Brian Q. Hutchings
3/8/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
3/8/14
Read Re: John Gabriel's Thread on Mathematics.
Brian Q. Hutchings
3/8/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
3/8/14
Read Re: John Gabriel's Thread on Mathematics.
Brian Q. Hutchings
3/8/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
3/8/14
Read Re: John Gabriel's Thread on Mathematics.
Brian Q. Hutchings
3/8/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
3/9/14
Read Re: John Gabriel's Thread on Mathematics.
thenewcalculus@gmail.com
3/11/14
Read Re: John Gabriel's Thread on Mathematics.
Hoofington P. McSnort
3/11/14
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thenewcalculus@gmail.com
3/11/14
Read Re: John Gabriel's Thread on Mathematics.
Wizard-Of-Oz
3/11/14
Read Re: John Gabriel's Thread on Mathematics.
Brian Q. Hutchings
3/11/14
Read hrea
Brian Q. Hutchings
3/12/14
Read Re: hrea
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