On Monday, October 9, 2017 at 11:16:44 AM UTC+3, Zelos Malum wrote: > >Define what is the null sequence you a real Troll? wonder! > > Depends a tad on what construction but for rationls, a null sequence is a cauchy sequence such that for a given \epsilon>0, we can find an N such that when m>N, we have |a_m|<\epsilon > > That is a null sequence. > > > there isn't any p'th root for any prime number moron (except in the fictional well-fabricated and established mathematics), where (p) is an odd prime number > > There is, again, use newton raphner method of root finding and you get a cauchy sequence that gives us the real number which is the root. > > > If you can't understand the simplest proofs presented and Published here, then you can't understand any logical result or conclusion > > I understand your proofs, they are fundamentally flawed. You are equating exist with a compass and straightedge construction, which is fallacious. If you said "There is no compass and straightedge construction for roots beyond n=2" to which I would say "Congratulation, you figure out something that has been known for 2 centuries" > > You are dishonest in misrepresenting your claims.
No, and not necessarily straightedge and unmarked ruler and compass construction for sure
IT is too.... simple for any clever school student to notice that Cauchy sequence is a set of distinct rational numbers (n_i)/(m_i), where (i) is positive integer say (1, 2, 3, ..., i), representing the order sequence, and (n_i), (m_i) are integers where simply they choose sufficiently a rational number to express their irrational number or fraction expansion and there isn't any other way (except in their minds) as assuming the sequence is going to infinity, but infinity doesn't exist basically and their representation would remain forever as a rational number as a ratio of two large integers, where at the same time the chosen large integers are not accepted to have infinite sequence of digits or terms (since they become undefined and also actually impossible)
Can't you ANALYSE it and see it yourself so easily considering the transcendental number (e) for instance as this:
e =/= 2 e =/= (2.7 = 27/10) e =/= (2.71 = 271/100) e =/= (2.718 = 2178/1000) e =/= (2.7182 = 27182/10000) e =/= (2.71828 = 271828/100000) e =/= (2.718281 = 2718281/1000000) e =/= (2.7182818 = 27182818/10000000) e =/= (2.71828182 = 271828182/100000000) ..... .....
By VERY little induction and very LITTLE common sense (that every mathematician and any layperson or a sheered boy must acquire), we firmly conclude and prove beyond any little doubt that
e =/= NOTHING
since no end by definition, and nothing is like your alleged infinity that isn't any number nor anything else but non-existing
Same applies to any number (with endless terms or digits), wither it is a real fraction ENDLESS expansion or a real constructible number endless representation or any other types of many alleged real FICTIONAL endless irrational numbers, for sure
But how would the unnecessary Daily business of mathematics runs if they confess the facts so openly
But still, we need that oldest deceptive number (Pi) for APPROXIMATING (in constructible numbers ONLY-since no other way) the area of our regular constructible polygon (that we might think as a circle)
I had been explaining this simplest fact with few others for years now, but alas no hope unless the alleged masters of mathematics (naturally from very reputable universities) write it to you in few thousands of papers and so many books with tons of fabricated old references as usual, and the business of mathematics would boom much faster than ever
And keep this for future records to remember for sure