An uncountable countable set
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From: Han de Bruijn on 15 Sep 2006 06:00 mueckenh(a)rz.fh-augsburg.de wrote: > Virgil schrieb: > >>Counting can be done by making tally marks or moving pebbles, for >>example, entirely without numbers, though we have become so >>sophisticated that we may have trouble realizing it. >> >>It is whether the tally marks or collected pebbles biject with the >>objects counted which is the issue. >> >>And no number need ever be mentioned or used. > > Your tally marks and moving pebbles are numbers. Get more sophisticated > in order to see it. Precisely! Mathematicians get confused by the idea of a "bijection", which is an Equivalence Relation, which in turn is a "generalization" of "common equality" (yes: the one in a = b). But the funny thing is that EQUALITY HAS NEVER BEEN DEFINED. So there is actually nothing to "generalize". Equivalence relations are a "generalization" of nothing. But, fortunately, reality is more simple than this. Every equality is an equivalence relation. And every equivalence relation is an equality. So the bijection between tally marks or collected pebbles with counted objects means, indeed, that tally marks and moving pebbles ARE numbers. Han de Bruijn
From: Han de Bruijn on 15 Sep 2006 06:05 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
From: Mike Kelly on 15 Sep 2006 06:20 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. -- mike.
From: Han de Bruijn on 15 Sep 2006 06:34 Mike Kelly wrote: > So you still don't know what "probability" means. On the contrary. Very much better than you. > How predictable. Same to you. No? Han de Bruijn
From: Mike Kelly on 15 Sep 2006 06:48
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? 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? > > 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. -- mike. |