An uncountable countable set
in [Math]
|
Prev: integral problem
Next: Prime numbers
From: Tony Orlow on 15 Sep 2006 16:31 Mike Kelly wrote: > Han de Bruijn wrote: >> Han de Bruijn wrote: >>> Mike Kelly wrote: >>>> 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. > > Please don't snip this necessary context. > >>> So you still don't know what "probability" means. >> On the contrary. Very much better than you. > > Interesting. What do you base this claim on? Unabashed and unjustified > egotism? I think Han brought up a good point in Calculus XOR Probability. > > 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? Does the set of naturals with property P have a mapping function from the naturals? :) > >>> How predictable. >> Same to you. No? > > Sure, posting rubbish about a subject one knows too little about is > liable to get one called out by someone or other. > Yes, you might want to watch that, Mike.
From: Tony Orlow on 15 Sep 2006 16:41 stephen(a)nomail.com wrote: > Han de Bruijn <Han.deBruijn(a)dto.tudelft.nl> wrote: >> mueckenh(a)rz.fh-augsburg.de wrote: > >>> Representation is number. There is no difference. Numerals have no >>> "soul". > >> Whew! I've never heard someone expressing this fact so lucidly! > >> Han de Bruijn > > So 3/2 is a different number than 6/4? The representations > differ, and if there is no difference between representation > and number, then different representations must imply different > numbers. For that matter 6 birds is a different representation > of 6 than 6 cars. And 6 birds is a different representation > of 6 than 6 different birds? How many 6's are there? > > Stephen > So, you are saying that, in some context, those two strings represent the same object? What is that context, and what is the object in that context?
From: MoeBlee on 15 Sep 2006 16:45 Tony Orlow wrote: > David R Tribble wrote: > > Tony Orlow wrote: > >>> Yes, I am including infinite values on the number line, since it's > >>> "infinitely long". > > > > David R Tribble wrote: > >>> Yet another thing you have to define or prove. Where do these > >>> "infinite values" appear on your real number line? > > > > Tony Orlow wrote: > >> Further from 0 than any finite number. > > > > Then how are they "on" the same "line"? > > > > By trichotomy. For all x ad y on the line, either x>y, x=y or x<y. > That's what makes a line in concept. That's question begging. Indeed, trichotomy is necessary for an ordering to be linear. But you have not proven the existence of such an ordering with the values you claim to be in its field. Just saying that your claim follows from trichotomy is just assuming what you are being asked to show, viz. that there is such a linear ordering with the values you claim to be in its field. But more basically, it doesn't matter, since you have no axiomatization nor rules of inference upon which to prove anything whatsoever in a mathematical system. MoeBlee
From: Tony Orlow on 15 Sep 2006 16:46 Randy Poe wrote: > Tony Orlow wrote: >> Haha!! Good one. "There are the same number of primes as there are >> naturals, a proper superset." Good answer. > > Obviously you don't believe that. Good guess. > > Here's an equivalent statement: If n is a natural, > there is an n-th prime. > > Do you think that's false? Do you think that there > is a natural n such that there is an (n-1)th prime, > but no n-th prime? No, I don't think that, but I do recognize that the set of primes is a subset of the naturals which proportion thereof has a limit of 0 as the range of the naturals approaches oo. Do you honestly think bijection works as an infinite analog to equality? Can a dense set like the rationals, with an infinite number of them between any two naturals, really be no greater a set than the naturals, which are an infinitesimal portion of the rationals? That's just poppycock. > > - Randy >
From: MoeBlee on 15 Sep 2006 16:52
Tony Orlow wrote: > Unbounded but finite may > be considered potentially, but not actually, infinite. That will be jiffy, once you give axioms and/or our definitions for 'potentially infinite' and 'actual infinite'. Until then, it's pure handwaving. MoeBlee |