PROOF INFINITY DOES NOT EXIST! Not even ONE type
in [Math]
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From: hagman on 10 Jul 2010 06:53 On 9 Jul., 02:43, "|-|ercules" <radgray...(a)yahoo.com> wrote: > A REVISED PROOF OF THE NON-EXISTENCE OF INFINITY > > C10 = 0.12345678910111213141516... > > x = the number of digits in the expansion of C10 > y = the number of consecutive digits of PI in C10 > > As x->oo, y->oo > x = oo > > Assume the limit exists. > y=oo > Contradiction (for each finite starting digit of PI in C10 there is a finite ending digit) > Limit doesn't exist. There is a great difference between lim_{n->oo} f(n) = oo and E n in NN: f(n) = oo The former simply states that for all m in NN there is a k in NN such that for all n>k we have f(n) > m. OTOH, the latter states that there are n where f(n) has a value that isn't even a number. > > y cannot reach infinity > therefore x cannot reach infinity For finite subsequences, there is clearly a maximum value of y that is attained (at least once). For the infinite sequence, the supremum of pi subsequence lengths need not be attained. > > x = the number of digits in the expansion of C10 > x =/= oo > > > > > INFERENCE there is no oo Non sequitur > > > Herc > > -- > > Conan do we REALLY have to hear the lamentations of the women? > >
From: |-|ercules on 10 Jul 2010 07:07 "hagman" <google(a)von-eitzen.de> wrote > For finite subsequences, there is clearly a maximum value of y that is > attained (at least once). > For the infinite sequence, the supremum of pi subsequence lengths need > not be attained. > I was thinking along those lines (so to speak) today but it would imply a bizarre conclusion. As x->oo, y->larger subsequence lengths Here's a simpler version: H1= 0.101101110111101111101111110... apologies if I borrowed someone's constant! So you're saying if H1 had an infinite amount of digits in it's expansion, the number of consecutive 1's would be (a non attainable non number?) Herc
From: Wolf K on 10 Jul 2010 09:47 On 09/07/2010 15:45, K_h wrote: [...] > [These] question[s] [don't] need to be answered in order to know that these truths > always exist. How does anything exist? How does the galaxy exist? People don't > need to have those answers to know that they exist. [...] In your posts, the term "exist" is vague and unclear. It also shifts meanings. Exactly which meaning of "exist" do you have in mind? Eg, the four uses of the term in the snippet I quoted are all different, and three of them are mutually exclusive (insofar as one can decode the probable intensions of the terms). The fourth asks about the meaning of the term itself. FWIW, I think Plato's ontological questions are so ill-formed that his answers aren't even wrong. cheers, wolf k.
From: George Greene on 10 Jul 2010 11:31 On Jul 9, 6:38 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > Perhaps you don't understand the proof, it only contradicts a well used axiom, not a well established fact. AND WHICH axiom is that?? If you can answer that one question (which if course you can't), we MIGHT get somewhere.
From: Wolf K on 10 Jul 2010 12:26
On 09/07/2010 18:42, |-|ercules wrote: [...] > > You have a point for once. Early definitions of formal systems were > "void of semantics". Historically false. The realsiation that formal languages have no content was arrived at over a period of centuries, and even today most people can't grasp the concept. [...] wolf k. |