In article <email@example.com>, Zeit Geist <firstname.lastname@example.org> wrote:
> On Tuesday, June 25, 2013 1:46:10 PM UTC-7, muec...@rz.fh-augsburg.de wrote: > > On Monday, 24 June 2013 21:44:48 UTC+2, Virgil wrote: > > > > > In article <email@example.com>, > > > firstname.lastname@example.org 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. > > > > Ordinal nor Cardindals form a metric spaces, but R does. > Hence, you can't use that form of the definition of limit here.
As a definition for limits, at least any standard notions of limits in analysis, it cannot be used anywhere, as it specifies only a necessary condition but fails to specify a sufficient condition even for a sequence of reals.
Such an oversight is Just one the mark of a mathematical incompetency. --