
Re: Discussion with WM  Frustration reaches boiling point (What is not clear?)
Posted:
Jul 5, 2014 2:00 PM


On 7/5/2014 10:48 AM, PotatoSauce wrote: > On Saturday, July 5, 2014 1:34:21 PM UTC4, muec...@rz.fhaugsburg.de wrote: >> On Saturday, 5 July 2014 17:14:53 UTC+2, PotatoSauce wrote: >> >> >> >> >> >>> >> >>> If you are assuming from the start N doesn't exist >> >> >> >> I do not. >> >> >> >>> to prove that there is no bijection between N and Q, then your logic is entirely off. >> >> >> >> I assume N to exist and to enumerate all rational numbers. Only mathematical reality of real analysis contradicts this assumption. That is called a proof by contradiction. >> >>> >> >>> >> >>> >> >>> You want lim card(s_n) to represent the cardinality of the sequence s_n "at infinity." >> >> >> >> I do not assume that a limit exists. But I show that the sets cannot get empty even if a limit exist. >> > > But you agreed that > > lim t>0 (t,0) u (0, t) = { }. > > You have also tacitly acknowledged that set limits pass through set relation, thus > > {} <= lim t>0 { t/2 } <= lim t> 0 (t,0) u (0, t) = {} > > (using <= for subset) > > So clearly, we can have nonempty sets with empty limit sets. > > >
And so clearly the other way?
You can see from topology running out either, I would hope.
Would you agree that there are definitions in topology? At all?

