An uncountable countable set
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From: Virgil on 19 Sep 2006 13:29 In article <1158665286.798016.156370(a)h48g2000cwc.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > Mike Kelly schrieb: > > > > Please make just the experiment. Choose at random 30 natural numbers > > > from the whole set N. What is the result? How many of these 30 numbers > > > are in fact divisible by 3? (In case you have problems with large > > > numbers: It is easy to check the divisibility of the number by checking > > > the divisibility of the sum of its decimal digits.) > > > > > > Now, it there a distribution lacking, or is the complete set of natural > > > numbers lacking? > > > > Neither. There is a lack of distribution *for the complete set*. > > If here is the set, than you do not need a distribution. If you have > access to each number, then select just blind by random choice. How do you guarantee that your version of "blind choice" gives each natural the same chance of being picked as any other? Do you roll an infinite sided die? About the closest one can come is, for some slightly positive epsilon, to give each n in {0,1,2,3,...} the probability (1-epsilon)*epsilon^n, so that any two successive naturals have nearly equal likelihood.
From: Virgil on 19 Sep 2006 13:34 In article <1158666375.530157.255170(a)m7g2000cwm.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > Mike Kelly schrieb: > > > > > All naturals do not exist. What is "all"? > > > > Huh? So some naturals don't exist? What does that mean? How can > > something that doesn't exist be a natural number? > > Not all novels do exist. Is that meaning clear to you? If it is clear to "Mueckenh", he must be suggesting that for naturals, like novels, more are being created every day. What new naturals were created yesterday, "Mueckenh"?
From: Virgil on 19 Sep 2006 13:37 In article <1158666824.392611.242720(a)d34g2000cwd.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > Mike Kelly schrieb: > > > > What bearing does empirical evidence have on what is mathematically > > meaningful? > > If mathematics states that III + II = IIIII, then it is true (at least > the result), and if it states otherwise, then it is false. That is very > easy and needs no axioms. Depends on what that notation rep[resents. If it is binary numerals, the decimal equivalent would be 7 + 3 = 31.
From: Tony Orlow on 19 Sep 2006 13:39 MoeBlee wrote: > Tony Orlow wrote: >> I am well aware my position is "provably false", but I am >> also aware that that depends on the axioms assumed and the rules >> regarding logical inference. > > No, your "position" is not coherent enough to be addressed as either > true or false. A bunch of gibberish doesn't admit of examination for > truth or falsehood. You are wrong. If I assert that S = proper_subset(T) -> |S|<|T|, then this is a basic axiom that one can accept which makes all of transfinitology untenable. > >> I don't know about Virgil, so maybe he IS wasting his >> time. > > His time at least SEEMS to me to be wasted with you. Meanwhile, I KNOW > that I'm wasting my time trying to reason with you. With what level of surety are you sure? There is always the chance that you will benefit, by at least momentarily entertaining my suggestions. When you begin to question the order of preference among basic questions, then you learn to do a little shuffling. > > MoeBlee >
From: Tony Orlow on 19 Sep 2006 13:42
MoeBlee wrote: > Han de Bruijn wrote: >> MoeBlee wrote: >> >>> 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. >> Come on, Moeblee, don't be silly! Let Google be your friend! > > I'm well aware of the notions of 'potential infinity' and 'actual > infinity' that go back through at least a couple thousand years of > philosophy and philosophy of mathematics. If you are so well-acquainted with these notions, could you be troubled to define a distinction between them? > But to use those notions in > an axiomatic mathematics requires either defining the terms > 'potentially infinite' and 'actually infinite' in the axiomatic theory > or taking them as primitive and giving axioms for them in the axiomatic > theory. So far, that has not been done in this thread or in any other > thread I've happened to read. It depends on the definition of an index for each element in an ordered set. > > Meanwhile, rather than direct you to an Internet search, I recommend > 'The Philosophy Of Set Theory' by Mary Tiles for more about 'potential > infinity' and 'actual infinity' and debates through history about > infinity. Thankz > > MoeBlee > |