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

 Messages: [ Previous | Next ]
 Rotwang Posts: 1,685 From: Swansea Registered: 7/26/06
Re: Warning to visitors to sci.math
Posted: Mar 13, 2012 6:18 PM

On 13/03/2012 01:16, DavidW wrote:
> Peter Moylan wrote:
>> [...]
>>
>> I'm in the Cantor camp myself. If you can't conceive of uncountable
>> infinities then measure theory has to be re-done from the bottom up,
>> and things like integration become conceptually harder. Not to mention
>> concepts like continuity, limits, and so on.

>
> 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.

Date Subject Author
3/7/12 DavidW
3/8/12 Brian Chandler
3/8/12 Richard Tobin
3/8/12 Shmuel (Seymour J.) Metz
3/8/12 amzoti
3/9/12 micky
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3/8/12 DavidW
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3/8/12 J. Antonio Perez M.
3/8/12 DavidW
3/8/12 J. Antonio Perez M.
3/9/12 DavidW
3/9/12 Brian Chandler
3/9/12 DavidW
3/9/12 DavidW
3/9/12 Brian Chandler
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3/9/12 Frederick Williams
3/9/12 DavidW
3/9/12 Frederick Williams
3/9/12 DavidW
3/9/12 J. Antonio Perez M.
3/10/12 Frederick Williams
3/10/12 DavidW
3/10/12 DavidW
3/10/12 Jerry Friedman
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3/10/12 Harrison Hill
3/12/12 Tom P
3/12/12 DavidW
3/12/12 Prai Jei
3/12/12 J. Antonio Perez M.
3/12/12 Peter Moylan
3/12/12 DavidW
3/13/12 Rotwang
3/13/12 DavidW
3/13/12 Rotwang
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3/14/12 DavidW
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3/12/12 Stan Brown
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3/14/12 Tim Little
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