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


Re: WM screws up the notion of a limit!
Posted:
Jun 26, 2013 5:46 PM


In article <01a9e048eeae45fb8a697dce459cf865@googlegroups.com>, mueckenh@rz.fhaugsburg.de wrote:
> On Tuesday, 25 June 2013 23:33:29 UTC+2, Zeit Geist wrote: > > Ordinal nor Cardindals form a metric spaces, but R does. Hence, you can't > > use that form of the definition of limit here. > > In mathematics I can use the definition the definition of limit and apply it > as follows: > lim{n>oo} min(100, Card(N \ F(n))) = 100. Which is totally irrelevant to the fact that what WM presented as the definition of every limiting process was not even valid for limits of sequences of real numbers, and was totally irrlevant to limits of sequences of sets.
Two obvious set limits are:
For an infinite sequence of sets that is increasing when ordered by inclusion, the limit is the union of all the sets in the sequence.
Thus Lim(FISDON(n)) = N
For an infinite sequence of sets that is decreasing when ordered by inclusion, the limit is the intersection of all the sets in the sequence.
Thus Lim(N\FISON(n))  {}
For infinite sequences of values in a topological space like the reals, for all but finitely many of the sequence values mut be in any neighborhood of a supposed limit value for to to be the actual limit. 

