Virgil
Posts:
8,833
Registered:
1/6/11


Re: WM screws up the notion of a limit!
Posted:
Jun 25, 2013 5:53 PM


In article <6759edbd15474ac19207634bbcd8864f@googlegroups.com>, mueckenh@rz.fhaugsburg.de wrote:
> On Monday, 24 June 2013 21:44:48 UTC+2, Virgil wrote: > > In article <a58bf1cddc69421191279172a7e8876d@googlegroups.com>, > > mueckenh@rz.fhaugsburg.de wrote: > > >> In mathematics every reasonable limit has to differ by less than any given > >> distance from infinitely many terms of the sequence. > > > That is a clearly corrupt and unworkable as a definition of limits, > > You can find the precise and workable definition in every text book including > three of mine. It excludes N as the limit of the sequence of FISONs. > Then each of WM's books contains lies about limits.
And If the above is his only definition of limits, omits mathematically well defined and ACCEPTED limits for sequences of sets.
As in https://en.wikipedia.org/wiki/Limit_superior_and_limit_inferior
While WM's statement above is a NECESSARY condition for the limit of a sequence of REAL NUMBERS to exist , it is NOT a sufficient condition, and thus grossly improper as a definition even for a sequence of real numbers.
According to WM's definition above, "every reasonable limit has to differ by less than any given distance from infinitely many terms of the sequence" the sequence of reals 0,1,0,1,0,1,... can have two "reasonable" limits,
And according to WM's definition above, "every reasonable limit has to differ by less than any given distance from infinitely many terms of the sequence" the set of all rational numbers, rearranged as a sequence, can have any and every real number as a reasonable limit. 

