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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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Rotwang

Posts: 1,685
From: Swansea
Registered: 7/26/06
Re: Warning to visitors to sci.math
Posted: Mar 13, 2012 6:18 PM
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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
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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
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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
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DavidW
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DavidW
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DavidW
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Frederick Williams
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DavidW
3/9/12
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Frederick Williams
3/9/12
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DavidW
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J. Antonio Perez M.
3/10/12
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3/12/12
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3/12/12
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3/13/12
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Rotwang
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3/14/12
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Horand.Gassmann@googlemail.com
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Lanarcam
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Richard Tobin
3/13/12
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Peter Moylan
3/14/12
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3/14/12
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3/14/12
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Rotwang
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3/16/12
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3/17/12
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3/17/12
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3/16/12
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3/10/12
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3/12/12
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3/11/12
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3/8/12
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