PROOF INFINITY DOES NOT EXIST! Not even ONE type
in [Math]
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From: George Greene on 7 Jul 2010 13:18 On Jul 6, 3:23 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > C10 = 0.12345678910111213141516... > > It contains pi, segmented. Well, gee, ..012345678901234567890123456789...... repeating forever ALSO contains Pi, segmented, OR ANY OTHER NUMBER, SEGMENTED, if you will allow a segment-length OF 1, DUMBASS. > You have to stop thinking of infinity > as a really long string for a moment, WE never STARTED thinking of "infinity" as that. A really long string is an infinite SUBSET. A REAL is represented as a really long string because it's an infinite SUBSET. > because there's no infinite string of pi inside root 2 or e etc. OF COURSE there is, SEGMENTED. > but the further you go along the string the > longer and longer sequences are found. SO WHAT?? NOBODY HAS EVER DISPUTED THIS! You can take a list OF FINITE strings and have it be true that the further down it you go, the more OF EVERY real or string hs occurred in it! This simply does not have anything to do with the existence of infinity. Infinity exists because there are an infinite number of natural numbers. Higher infinities exist because if those natural numbers form a set, then it has a powerset, and the powerset IS ALWAYS bigger!
From: Dan Christensen on 7 Jul 2010 13:36 On Jul 6, 3:23 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > > does Champernowne's constant contain pi? It does contain all finite digit > > sequences of pi. > > > - Tim > > C10 = 0.12345678910111213141516... > > It contains pi, segmented. > > You have to stop thinking of infinity as a really long string for a moment, because there's > no infinite string of pi inside root 2 or e etc. but the further you go along the string the > longer and longer sequences are found. > > ----------------------------------------------- > > 1/ there's no infinite sequence of pi's digits within C10 (every finite starting point has a finite ending point) > 2/ as the length of C10 digit expansion -> oo, the consecutive number of digits of pi -> oo > 3/ the length of C10 digit expansion is oo > 4/ the consecutive number of digits of pi = oo (3) -> (2) > > CONTRADICTION (1) & (4) > > THEREFORE no limit exists as the length of digit expansions (of any real) -> oo > > GENERALIZATION no limit exists as the length of sequences (of any type) -> oo > > INFERENCE there is no oo > Sorry, I can't follow your proof, but don't you think there might be something wrong with your system of axioms, whatever they may be? Infinity is no big deal. In natural number arithmetic for example, we just assume that if you add 1 to any number, the result will be another, larger number. Do you really think it is necessary to specify some arbitrary maximum number? Dan Download my DC Proof software http://www.dcproof.com
From: Curt Welch on 7 Jul 2010 14:36 George Greene <greeneg(a)email.unc.edu> wrote: > On Jul 6, 3:23=A0pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > Infinity exists because there are an infinite number of natural > numbers. > Higher infinities exist because if those natural numbers form a set, > then it has a powerset, and the powerset IS ALWAYS bigger! You have to be careful in such debates to understand what "exists" means and how you are using it. You can't prove that "infinity" exists by referencing the natural numbers if you can't first prove that the natural numbers "exist". There is physical existence which is the foundation of all types of existence. But math isn't about simple physical existence. It's about words and their definitions. It's a study of formal langauge and what can be _said_ using a formal language. It's not about physical existence beyond the physical existence of the langauge. Infinity as a physical object can be argued not to exist. But as a word in a formal language, it does exist. And in Math, if the word exists, and it's associated definition exists, then it exists in math. And we can, very easily, use words to define what we mean by infinite - so the concept does exist, even if it can't be used to label a physical object. It exists as a procedure which has no way to halt. (10 goto 10). The self referencing power of language then allows us to define an infinite number of different procedures which all never halt. And in that self reference, we defined (aka brought into existence) yet another type of infinity. But just becuase we can use the power of language to define these concepts, doesn't mean they are valid labels for real aspects of our physical universe. Math however is not about that. It's just about exploring what can be _said_ with a formal langauge. And with a formal langauge, we can define infinity, and higher orders of infinity. They exist in the language of mathematics, but may or may not, exist in any sense in the physical universe. You have to keep those two types of existence separate when studying and understanding mathematics. -- Curt Welch http://CurtWelch.Com/ curt(a)kcwc.com http://NewsReader.Com/
From: Aatu Koskensilta on 7 Jul 2010 14:31 curt(a)kcwc.com (Curt Welch) writes: > But math isn't about simple physical existence. It's about words and > their definitions. It's a study of formal langauge and what can be > _said_ using a formal language. No it's not. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: |-|ercules on 7 Jul 2010 18:30
"Aatu Koskensilta" <aatu.koskensilta(a)uta.fi> wrote ... > curt(a)kcwc.com (Curt Welch) writes: > >> But math isn't about simple physical existence. It's about words and >> their definitions. It's a study of formal langauge and what can be >> _said_ using a formal language. > > No it's not. A counter example? Herc |