```Date: Sep 29, 2017 1:15 AM
Author: zelos.malum@gmail.com
Subject: Re: Teaching mainstream morons about their own flawed theories:<br>  Every Cauchy sequence of real numbers converges to a limit.

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>Incorrect, if that point, which would be denoted as the limit, does not exist in the space in question, it doesn't converge.And a norm isn't a distance, even if it can be intepritated as such.A space can be real numbers, have them in it, etc, but doesn't need to so no assumption. As for reals, they are trivially constructed, you are just too stupid to understand it.Yes, you do too much scat, take your bedroom fetishes elsewhere. Some of us are trying to do something real.
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