*NEW DIGIT SEQUENCE* is an OXYMORON!
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From: Daryl McCullough on 14 Jun 2010 17:04 Graham Cooper says... >Computable sequences contain every digit of every Possible infinite >sequence Nobody said otherwise, and that has nothing to do with Cantor's proof. You are deeply confused. Cantor's theorem is: For any sequence of reals r_1, r_2, ..., there is a real d such that forall n, d is unequal to r_n. Your point about "computable sequences contain every digit of every possible infinite sequence" has *nothing* to do with Cantor's theorem. It's true, but irrelevant. The fact that you think it is relevant shows how completely confused you are. -- Daryl McCullough Ithaca, NY
From: Graham Cooper on 14 Jun 2010 17:43 On Jun 15, 7:04 am, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: > Graham Cooper says... > > >Computable sequences contain every digit of every Possible infinite > >sequence > > Nobody said otherwise, and that has nothing to do with Cantor's > proof. You are deeply confused. > > Cantor's theorem is: For any sequence of reals r_1, r_2, ..., there > is a real d such that forall n, d is unequal to r_n. > > Your point about "computable sequences contain every digit of every > possible infinite sequence" has *nothing* to do with Cantor's theorem. > It's true, but irrelevant. The fact that you think it is relevant shows > how completely confused you are. > > -- > Daryl McCullough > Ithaca, NY What does your antidiagonal look like? Give us an example. Describe it graphically Herc
From: Daryl McCullough on 14 Jun 2010 18:36 Graham Cooper says... >What does your antidiagonal look like? Haven't you been told that many times? >Give us an example. Describe it graphically You've been given examples, many times. -- Daryl McCullough Ithaca, NY
From: Tim Little on 14 Jun 2010 20:01 On 2010-06-14, |-|ercules <radgray123(a)yahoo.com> wrote: > Lists are not sets now? No. Lists are functions for which the domain is an initial segment of finite ordinals. You could model the function by a set of ordered pairs, and the domain and range of the function are sets, but lists in general are not the same thing as sets. - Tim
From: Tim Little on 14 Jun 2010 20:05
On 2010-06-14, |-|ercules <radgray123(a)yahoo.com> wrote: > Here is a counterintuitive argument about properties of infinite SETS and their ELEMENTS. > > In pure functional programming there is no repeated input, there is a single input > stream and there is some tricky redirection in order to process that stream interactively. [...] > In this context, > > 3 > 31 > 314 > 3141 > 31415 > ... > > and > > 31415... > > are 100% EQUIVALENT DATA. Distinctions that are present in mathematics are lost in mere programming models. > So when you consider the whole set, it DOES have a new property. > That all digit sequences are computable to infinite length. That is not true even in programming. You don't know the definition of "computable sequence" or what it means. - Tim |