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Topic: Warning to visitors to sci.math
Replies: 266   Last Post: Mar 19, 2012 9:13 AM

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DavidW

Posts: 274
Registered: 5/29/09
Re: Warning to visitors to sci.math
Posted: Mar 13, 2012 6:50 PM
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Rotwang wrote:
> On 13/03/2012 01:16, DavidW wrote:
>> I don't have a problem with calculus, limits, etc., or any sort of
>> convergence.

>
> You would do, if you actually understood them.
>
> Exercise: using what you claim are "the axioms of mathematics" (at
> http://2000clicks.com/mathhelp/BasicArithmetic.aspx), give a
> definition of the number e > 0 and show that it has the property that
> d/dx (e^x) = e^x. This will involve giving a definition of a^b for
> arbitrary real b and positive a, which has the usual properties which
> are required of exponentiation.
>
> Hint: the usual definition of e is as the least upper bound of the set
> of partial sums of the form sum_{i = 0}^n 1/n!, n in N. But since that
> set is infinite, and therefore not a set (according to you), the
> completeness axiom may not be used to show that such a least upper
> bound exists.


Does this come down to a quibble over what a set is? It's a converging infinite
series. The further you go the more accurate e is. I don't see any problem with
this.




Date Subject Author
3/7/12
Read Warning to visitors to sci.math
DavidW
3/7/12
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adamk
3/8/12
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Brian Chandler
3/8/12
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Richard Tobin
3/8/12
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Shmuel (Seymour J.) Metz
3/8/12
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amzoti
3/9/12
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micky
3/8/12
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Frederick Williams
3/8/12
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DavidW
3/8/12
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DavidW
3/8/12
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DavidW
3/8/12
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J. Antonio Perez M.
3/8/12
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DavidW
3/8/12
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J. Antonio Perez M.
3/9/12
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DavidW
3/9/12
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Brian Chandler
3/9/12
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DavidW
3/9/12
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DavidW
3/9/12
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Brian Chandler
3/9/12
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DavidW
3/9/12
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Frederick Williams
3/9/12
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DavidW
3/9/12
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Frederick Williams
3/9/12
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DavidW
3/9/12
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J. Antonio Perez M.
3/10/12
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Frederick Williams
3/10/12
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DavidW
3/10/12
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DavidW
3/10/12
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Jerry Friedman
3/10/12
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Don Phillipson
3/10/12
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Harrison Hill
3/12/12
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Tom P
3/12/12
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DavidW
3/12/12
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Prai Jei
3/12/12
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J. Antonio Perez M.
3/12/12
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Peter Moylan
3/12/12
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DavidW
3/13/12
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Rotwang
3/13/12
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DavidW
3/13/12
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Rotwang
3/13/12
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DavidW
3/13/12
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Rotwang
3/13/12
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DavidW
3/13/12
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Rotwang
3/13/12
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DavidW
3/13/12
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Rotwang
3/13/12
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DavidW
3/13/12
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Rotwang
3/14/12
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DavidW
3/14/12
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Rotwang
3/14/12
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J. Antonio Perez M.
3/14/12
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DavidW
3/14/12
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Horand.Gassmann@googlemail.com
3/14/12
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J. Antonio Perez M.
3/14/12
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DavidW
3/14/12
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3/14/12
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DavidW
3/14/12
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J. Antonio Perez M.
3/14/12
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DavidW
3/14/12
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Rotwang
3/14/12
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DavidW
3/14/12
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Rotwang
3/15/12
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Jussi Piitulainen
3/15/12
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DavidW
3/14/12
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Rotwang
3/14/12
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DavidW
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Rotwang
3/14/12
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DavidW
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3/14/12
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DavidW
3/14/12
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Rotwang
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DavidW
3/15/12
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Rotwang
3/15/12
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DavidW
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3/15/12
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DavidW
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DavidW
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DavidW
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DavidW
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DavidW
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DavidW
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ross.finlayson@gmail.com
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Daryl McCullough
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Prai Jei
3/14/12
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Transfer Principle
3/15/12
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FredJeffries@gmail.com
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Transfer Principle
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Daryl McCullough
3/16/12
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J. Antonio Perez M.
3/14/12
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ross.finlayson@gmail.com
3/12/12
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Stan Brown
3/13/12
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3/13/12
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3/13/12
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Daryl McCullough
3/13/12
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3/13/12
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3/13/12
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3/13/12
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3/13/12
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J. Antonio Perez M.
3/13/12
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Richard Tobin
3/13/12
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Peter Moylan
3/14/12
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R H Draney
3/14/12
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Transfer Principle
3/14/12
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3/15/12
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3/15/12
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3/14/12
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3/14/12
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J. Antonio Perez M.
3/15/12
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Transfer Principle
3/16/12
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Daryl McCullough
3/17/12
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Michael Stemper
3/17/12
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3/14/12
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Michael Stemper
3/14/12
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3/13/12
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3/13/12
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3/13/12
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DavidW
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J. Antonio Perez M.
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DavidW
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J. Antonio Perez M.
3/14/12
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3/14/12
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DavidW
3/13/12
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Jim Burns
3/14/12
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3/14/12
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Transfer Principle
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3/14/12
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J. Antonio Perez M.
3/15/12
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Transfer Principle
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3/15/12
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Transfer Principle
3/15/12
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3/15/12
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3/16/12
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quasi
3/16/12
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3/16/12
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quasi
3/15/12
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Daryl McCullough
3/10/12
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Prai Jei
3/12/12
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Peter Moylan
3/12/12
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DavidW
3/13/12
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Jim Burns
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Prai Jei
3/13/12
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FredJeffries@gmail.com
3/14/12
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Peter Moylan
3/10/12
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Stan Brown
3/11/12
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DavidW
3/12/12
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3/9/12
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Frederick Williams
3/8/12
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Transfer Principle
3/8/12
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J. Antonio Perez M.
3/8/12
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Daryl McCullough
3/10/12
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3/10/12
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DavidW
3/10/12
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3/10/12
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3/10/12
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J. Antonio Perez M.
3/11/12
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3/11/12
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3/11/12
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3/11/12
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3/11/12
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3/11/12
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3/11/12
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3/11/12
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3/11/12
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3/11/12
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3/12/12
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quasi
3/12/12
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quasi
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DavidW
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3/12/12
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DavidW
3/12/12
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quasi
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quasi
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3/12/12
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DavidW
3/12/12
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3/12/12
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quasi
3/12/12
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DavidW
3/12/12
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Frederick Williams
3/12/12
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DavidW
3/12/12
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Brian Chandler
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DavidW
3/12/12
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J. Antonio Perez M.
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DavidW
3/12/12
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DavidW
3/12/12
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J. Antonio Perez M.
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DavidW
3/13/12
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Michael Stemper
3/13/12
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DavidW
3/13/12
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Frederick Williams
3/13/12
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J. Antonio Perez M.
3/13/12
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DavidW
3/13/12
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3/12/12
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3/12/12
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Transfer Principle
3/12/12
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3/12/12
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Transfer Principle
3/13/12
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FredJeffries@gmail.com
3/15/12
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3/10/12
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3/10/12
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3/9/12
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3/9/12
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DavidW
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quasi
3/9/12
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DavidW
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3/9/12
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Michael Stemper
3/9/12
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Jesse F. Hughes
3/9/12
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DavidW
3/10/12
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3/10/12
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FredJeffries@gmail.com
3/13/12
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Michael Stemper
3/14/12
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Transfer Principle
3/14/12
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J. Antonio Perez M.
3/14/12
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3/15/12
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3/15/12
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Daryl McCullough
3/19/12
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3/9/12
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3/9/12
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DavidW
3/10/12
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3/9/12
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3/9/12
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3/9/12
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3/8/12
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3/13/12
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3/16/12
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