An uncountable countable set
in [Math]
|
Prev: integral problem
Next: Prime numbers
From: Han de Bruijn on 15 Sep 2006 07:36 Mike Kelly wrote: > Han de Bruijn wrote about his understanding of probability: >> On the contrary. Very much better than you. > > Interesting. What do you base this claim on? Unabashed and unjustified > egotism? Look who is talking ... Unabashed and unjustified plagiarism? > Perhaps to demonstrate your firm grasp of these matters you could > define "probability" and then explain how one determines the > "probability" that "a natural" has some property P? This has been discussed at length. I'm not going to repeat anything. Han de Bruijn
From: mueckenh on 15 Sep 2006 08:46 Dik T. Winter schrieb: > > Index = natural number. There is no infinite index, because indexing is > > identifying. > > That does *not* explain why the list contains all numbers that can be > indexed. Let m be a unary number with m 1's, and n a list number with n 1's. If E n >= m, then m is in the list and can be indexed completely by list numbers. If not E n >= m, then m is not in the list and cannot be indexed completely by list numbers. Regards, WM
From: mueckenh on 15 Sep 2006 09:02 Mike Kelly schrieb: > Han de Bruijn wrote: > > mueckenh(a)rz.fh-augsburg.de wrote: > > > > > David R Tribble schrieb: > > > > > >>Tony Orlow wrote: > > >> > > >>>Wolfgang's and my position is that N is unbounded but finite, > > >> > > >>"Unbounded but finite" is a contradiction, meaning "not finite but > > >>finite". I'm sure you and Wolfgang think this double-think makes > > >>sense, but the rest of us don't. > > > > > > Your position only reflects the miseducation in mathematics during the > > > last decades. > > > > > > Actual or finished infinity is a contradicton. Surpassed infinity is a > > > contradiction. > > > > > > Unbounded but finite is mathematical reality. Think of the set of all > > > natural numbers which have been realized by writing down these numbers. > > > Think of the set of known prime numbers. Think of the set of written > > > novels. Think of the set of postings. > > > > > > These sets are unbounded because they can be extended without end. > > > Nevertheless they are always finite. > > > > Sorry for jumping in so late. But VM is quite right, of course. We have > > encoutered utterly absurd consequences of thinking otherwise, like the > > mainstream "theorem" that the probability of a natural being a multiple > > of 3 doesn't exist. While the obvious truth is that it is equal to 1/3 . > > > > This topic has been discussed at length in a thread called "Calculus XOR > > Probability". Let Google be your friend, eventually. > > > > Han de Bruijn > > So you still don't know what "probability" means. How predictable. Sorry, would you agree with me that the probability to take a natural number divisible by 3 from a box contaning the numbers from 1 to 9 is just 1/3? Would this probability change if the box contained the numbers from 1 to 900 or to 90000? Would it significantly change if the box contained the numbers from 1 to 100000? If you agree with me up to that point, then it is clear that the chance remains the same if we have all natural numbers in that box (provided, "all natural numbers" is a meaningful expression). The mathematics of the infinite can only be derived from the mathematics of the finite (because nobody has an idea what "the infinite" is). Otherwise the limit of the sequence 1/n might be 100. Nobody could prove that false. Regards, WM
From: Mike Kelly on 15 Sep 2006 09:22 Han de Bruijn wrote: > Mike Kelly wrote: > > > Han de Bruijn wrote about his understanding of probability: > > >> On the contrary. Very much better than you. > > > > Interesting. What do you base this claim on? Unabashed and unjustified > > egotism? > > Look who is talking ... Unabashed and unjustified plagiarism? Plagiarism? I don't get it. Who is plagiarising what? > > Perhaps to demonstrate your firm grasp of these matters you could > > define "probability" and then explain how one determines the > > "probability" that "a natural" has some property P? > > This has been discussed at length. I'm not going to repeat anything. I don't think 'discussed' is quite the right word. No matter, as your refusal admits that you are unable to justify your ludicrous claims about "obvious truth" vs. "theorems" (see, I can use "scare quotes", too!). -- mike.
From: Han de Bruijn on 15 Sep 2006 09:39
Mike Kelly wrote: > Han de Bruijn wrote: > > Plagiarism? I don't get it. Who is plagiarising what? "Your" would-be arguments against mine are not really yours. They are just a _plagiary_ of well-known "arguments" employed by the mainstream mathematics community. Han de Bruijn |