Re: Cantorian pseudomathematics

Han de Bruijn wrote:
> Toni Lassila wrote:
> >
> > On the other hand, for all your claims about wanting to make
> > mathematics more physical and applicable, you've not shown one actual
> > working method of simulating uniformly distributed naturals.
>
> If you can simulate them at any _finite_ interval (1,2,3,4,5,...,n)
> then you can simulate then at _all_ of those intervals, hence at the
> naturals.

If n is some finite natural, call a natural x in the interval [1..n]
"small" if 2*x is a also a member of [1.. n]; and call it "big"
otherwise.

Clearly, P(x is "big" | n) = floor(n/2)/n -> 1/2 as n -> oo; so, upon
taking the limit as Han does, P(arbitrary natural is "big") = 1/2; so
the odds that a random number is "big" are 50/50.

Thus Han's random natural generator should provide us, on average, with
equal numbers of "big" and "small" naturals.

Is 10^10^100 a "big" number? 2*10^10^100 is clearly included in the
interval (lim n->oo [1..n]), and so it should be "small" by definition.

Come to think of it - what is the smallest "big" number? I guess we'll
have to wait for Han's random natural generator to get up and running
before we can at least put a statistical upper bound on this...

Cheers - Chas

.

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