An uncountable countable set
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From: Han de Bruijn on 18 Sep 2006 05:43 Virgil wrote: > In article <450c7444(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > >>Virgil wrote: >> >>>In article <450c6210(a)news2.lightlink.com>, >>> Tony Orlow <tony(a)lightlink.com> wrote: > >>>>Let's use 1/aleph_0 for r and see what happens. >>> >>>Since probabilities are necessarily real numbers and 1/aleph_0, whatever >>>it may be, is not a real number, it is also not a probability. >> >>Oh Papa San Grasshopper Grampa Boyeeee! Man! That's so cute. What is a >>probability? A real between 0 and 1? > > Inclusive. > >>Does 1/aleph_0 lie within the real interval [0,1]? > > AS "1/aleph_0" is not a real number at all, and real intervals contain > nothing other than real numbers, "1/aleph_0" does not lie within ANY > real interval. Indeed. But if aleph_0 is considered as a finite quantity in infinite disguise, then I can nevertheless attach a meaning to TO's babblings. Han de Bruijn
From: Han de Bruijn on 18 Sep 2006 05:50 Virgil wrote: > It doesn't matter what TO tries to say about it, it still will not make > either aleph_0 into a real number, nor any alleged reciprocal of aleph_0 > into a real number. TO's aleph_0 is obviously different from yours. What he means is that the reciprocal of an infinitely large natural number is an infinitely small real number, as every engineer knows. Infinitely large/small is just "very" large/small in engineering terms, but I know that is very much "undefined" in mainstream mathematics. (I know, I know ...) Han de Bruijn
From: Han de Bruijn on 18 Sep 2006 06:05 Mike Kelly wrote: > Han.deBruijn(a)DTO.TUDelft.NL wrote: > >>What I meant to express is that you are about to be parrotting >>mainstream arguments, without adding to it much thoughts of >>yourself. And that is quite senseless because we have gone >>through all this already. > > Yes, and your position was utterly ripped apart in the very first > response to you by David C. Ullrich, and then by several others. You > were unable to defend your claim. So, why repeat it as though it were > in any way valid? That's because I did a _honest attempt_ to fit my position into the framework of nonstandard analysis (Robinson's theory), which failed. Of course it failed. Mainstream mathematicians have never understood how infinitesimals work. Han de Bruijn
From: Han de Bruijn on 18 Sep 2006 06:12 Mike Kelly wrote: > Han.deBruijn(a)DTO.TUDelft.NL wrote: > >>Mike Kelly wrote: >> >>>Given that any second-year student of probability theory knows that >>>there are no uniform distributions over countable sample spaces, [ ... ] >> >>This "given" is most disturbing. Mainstream mathematics is so certain >>about its own right that no sensible debate is possible. > > Please stop snipping so much context. It is dishonest. Why ?! Everybody should be able to look up the rest in the first place. I'm just snipping the parts that don't belong to the subject "Given ... blah .." Nothing dishonest, just sizing down the universe of discourse. Han de Bruijn
From: Han de Bruijn on 18 Sep 2006 06:20
Mike Kelly wrote [ dishonestly snipping again ]: > I haven't questioned your ability to use the calculus. Now use your common sense. Why would somebody who clearly has _some_ mathematical abilities be a complete crank if it comes to a subject which is somewhat different from calculus, but still is mathematics? Han de Bruijn |