Den fredag 29 september 2017 kl. 07:19:44 UTC+2 skrev Zelos Malum: > Den torsdag 28 september 2017 kl. 13:08:43 UTC+2 skrev John Gabriel: > > On Thursday, 28 September 2017 01:22:36 UTC-4, Zelos Malum wrote: > > > >For example the brainwashed moron Klyver will harp on the irrelevant fact that a Cauchy sequence of rationals may not converge to a rational number, BUT this does not mean the sequence does not converge because ALL Cauchy sequences WITHOUT ANY EXCEPTIONS converge. > > > > > > Incorrect, the fact that it doens't converge to a rational number means it doesn't converge in the rationals. Therefore by definition it is DIVERGENT! > > > > No moron. You don't understand. Just like you have never been able to understand. ALL Cauchy sequences converge to some magnitude/distance which is called a LIMIT. A moron like you and mainstreamers calling it a space does not change anything about its convergence. A Cauchy sequence will always CONVERGE to a LIMIT. This is why the very definition is stated in terms of magnitudes/distances, that is, |a_m - a_n|. That modulus is a **distance** you monkey! > > > > No amount of categorisation will change that. Spaces have ZERO to with it. In fact your head is so far up your arse that you don't realise your hilarious spaces assume the existence of elements which you haven't been able to establish, viz. "real" number. Thus most of your whimsical notions are a result of your mushy brain. Between your ears there is nothing but shit. > > > > I shall continue to punish you and the mainstream ruthlessly. I want you all doing a job that you are capable of doing - cleaning public toilets. On second thoughts you are probably so dirty also in your personal hygiene, you will need to be trained in this also. > > > > <too much scat and no time to ridicule moron> > > I understand cauchy sequences much better than you because I understand that just because Q<R doesn't mean that Q=R > > For your statement to be true, just must be able to find a rational number, such that it's square is equal to 2. Otherwise the sequence that tends toward it is divergent in Q. > > In R we can find the element, but we are talking in Q and Q alone, you cannot go outside of Q when it is Q we are talking about.
It's a bit like keep insisting Washington is the state capital when we are in fact talking about Texas alone.