>"John Gabriel" <email@example.com> wrote in message >news:firstname.lastname@example.org... >I receive a lot of visitors from St. Andrews university. Here is one of >their web pages:
>"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.