
Re: Teaching mainstream morons about their own flawed theories: Every Cauchy sequence of real numbers converges to a limit.
Posted:
Oct 4, 2017 6:48 AM


On Wednesday, 27 September 2017 09:53:39 UTC4, John Gabriel wrote: > "Every Cauchy sequence of real numbers converges to a limit." > > http://math.caltech.edu/~nets/lecture4.pdf > > In spite of this, you will get thousands of morons (Klyver and "Me" and Burse included) talking about Q as if it is not part of R. > > 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. > > Thus, if every Cauchy sequence converges to some *LIMIT*, then the limit must be DEFINED in each case. Well, to mainstream morons the circularity of their definitions is oblivious because syphilitic brains are unable to think properly. > > Carl Boyer summed it up best: > > "Cauchy had stated in his Cours d'analyse that irrational numbers are to be regarded as the limits of sequences of rational numbers. Since a limit is defined as a number to which the terms of the sequence approach in such a way that ultimately the difference between this number and the terms of the sequence can be made less than any given number, the existence of the irrational number depends, in the definition of limit, upon the known existence, and hence the prior definition, of the very quantity whose definition is being attempted. > > > That is, one cannot define the number sqrt(2) as the limit of the sequence 1, 1.4, 1.41, 1.414, ... because to prove that this sequence has a limit one must assume, in view of the definitions of limits and convergence, the existence of this number as previously demonstrated or defined. Cauchy appears not to have noticed the circularity of the reasoning in this connection, but tacitly assumed that every sequence converging within itself has a limit." > > The History of Calculus and its Conceptual Development' (Page. 281) Carl B. Boyer > > Orangutan academics will try to adorn their recognition of patters in series. By stating an observation about Cauchy sequences whose main attribute is a LIMIT (Because guess what you infinitely stupid imbeciles? You don't have convergence without a LIMIT. A limit in a Cauchy sequence is equivalent to the expression "UPPER BOUND" or "LOWER BOUND") using symbols, they imagine themselves to be sophisticated or "formal". > > Chuckle. I suppose that stating a definition without symbols is like attending a meeting in jeans and tshirt, whereas the meeting is attending in a suit when symbols are used. Only problem is that a monkey in a suit is a monkey no less. > > > The Informal Definition: > A sequence of rational numbers is called Cauchy if for any random value, say ? and an index N into the sequence, the distance between any two consecutive terms whose indexes are both greater than N, is less than ?. > > Now for the "formal" definition: > > A sequence of real numbers {a_n} is a Cauchy sequence provided that for every ? > 0, there is a natural number N so that when n, m ? N, we have that.  a_n ? a_m.  ? ?. > > Moron Klyver pay attention! It says "sequence of real numbers", but there are never any other sequences besides those of "rational numbers". Did you get this you baboon? Chuckle. It is irrelevant whether a sequence converges in the rationals or the mythical "reals". > > Comments are unwelcome and will be ignored. > > Posted on this newsgroup in the interests of public education and to eradicate ignorance and stupidity from mainstream mythmatics. > > gilstrang@gmail.com (MIT) > huizenga@psu.edu (HARVARD) > andersk@mit.edu (MIT) > david.ullrich@math.okstate.edu (David Ullrich) > djoyce@clarku.edu > markcc@gmail.com
Even "Me" has finally understood that my definition is a D. Cut.
L={1 < x < pi} and R={pi < x < 4} where x \in Q
is a valid D Cut.
You can choose any other elements m and n such that m < pi < n and it will conform as follows:
L={m < x < pi} and R={pi < x < n} where x \in Q
END OF DISCUSSION.

