
Re: Discussion with WM  Frustration reaches boiling point (What is not clear?)
Posted:
Jul 5, 2014 2:32 PM


On 7/5/2014 11:19 AM, PotatoSauce wrote: > On Saturday, July 5, 2014 2:00:03 PM UTC4, Ross A. Finlayson wrote: >> 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? > > This is from a previous discussion. We have established that we are using the standard product topology on sets, and I was just reiterating parts that WM has previously agreed to. >
As long as you'd agree:
1) that's a definition 2) there are others 3) there are usual "counterexamples in topology" a) definition of open and closed b) vacuity of c) contradictions in empty closures from nonempty

