In article <email@example.com>, firstname.lastname@example.org wrote:
> On Wednesday, 26 June 2013 00:01:32 UTC+2, Virgil 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. > > > 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. > > I need not show more than that this necessary condition is violated by the > asserted limit oo of the sequence a_n = 1/Card(|N\F(n)).
Then your claim that those a_n have such a limit is a false claim.
In fact, 1/Card(|N\F(n)) is not defined in normal real arithmetic, or any arithmetic in which delta-epsilonics is valid.
> The asserted limit > oo differs by oo from every term of the sequence.
The asserted limit is asserted only in WM's wild weird world of WMytheology and that assertion is certainly invalid elsewhere. --