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Topic: 2.43 - Cauchy sequences of rationals do not define real numbers.
Replies: 9   Last Post: Aug 3, 2014 12:19 PM

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 Andy C Posts: 107 Registered: 12/13/04
Re: 2.43 - Cauchy sequences of rationals do not define real numbers.
Posted: Aug 1, 2014 9:15 AM

>"John Gabriel" <thenewcalculus@gmail.com> wrote in message
>I receive a lot of visitors from St. Andrews university. Here is one of
>their web pages:

http://www-history.mcs.st-and.ac.uk/~john/analysis/Lectures/L10.html

>It states:

>"One of the problems with deciding if a sequence is convergent, is that you
>need to have a limit before you can test the definition."

>"One of the problems" ?!! That's an understatement! It is the main
>problem.

>That one can determine if a sequence is Cauchy or not, does not mean it has
>a limit.

>So, anyway, they define a Cauchy sequence and then further down the page:

>"The Main Result about Cauchy sequences - A Real Cauchy sequence is
>convergent."

>They haven't defined "real" number yet, but now suddenly a Cauchy sequence
>is convergent in R. Obvious circularity which the morons missed. They talk
>about convergence in R, even before they have defined R as a sequence of
>rational numbers. About as close as they came, was to state that a Cauchy
>sequence is bounded. Hilarious.

>Cauchy sequences of rationals do NOT define real numbers.

>Comments are NOT welcome. This comment is produced in the interests of
>public education; and to eradicate ignorance and stupidity from mainstream
>mythmatics.

Please see a mental health professional as soon as possible. This comment is
produced in the interests of public education; and to encourage John Gabriel
to get the mental health treatment he needs.

Date Subject Author
8/1/14 Andy C
8/1/14 David C. Ullrich
8/2/14 David C. Ullrich
8/2/14 David C. Ullrich
8/3/14 David C. Ullrich
8/1/14 El Problemo