Re: Cardinality question

"David C. Ullrich"
>LH
> >But I've also seen (unless I'm getting paranoid, which is quite
> >possible) that some computer people have picked up
> >mannerisms such as
> >"depends on the Axiom of Choice"
> >"in first-order logic"
> >"constructive mathematics".
>
> I don't see how that indicates that there's an "anti-Cantor"
> movement.
Okay, "anti-Cantor" is a misleading name. I used the slogan
"Cantor was wrong" simply because that is crank-dot-net's
name for this category of dispute, and iconoclasts and cranks
are always name-dropping, and in this case Cantor's name
is the one they go for. In the same class of dispute, but
more elementary, and not about Cantor at all, are claims
like 0.99999... <> 1.
>
> >Teaching math to computers is proving to be difficult. You've
> >probably heard of efforts at DARPA and the EU to spell out
> >a format for mathematical results, so that theorems can be
> >stored and linked linked just like modules in a computer
> >program. Easier said than done, and my theory is that a
> >resentment of things like cardinals is one of the results of
> >frustration. But again, it might be paranoia on my part.
>
> Of course teaching math to computers is difficult. But
> I don't see how that has anything to do with infinity.
> When _people_ prove things about infinite this and that
> they use finitely long arguments, and I don't see why
> formalizing arguments about infinite sets so that a
> computer can "understand" them should be any harder
> than doing the same thing with any other branch of
> mathematics.
E.g. defining a specific irrational number as a certain
partition of the infinite ordered set of rationals -- that's
hard to "code", and there's no way any computer will
ever verify the infinitely many inequalities that are
implicit in that partition. And it gets worse, I hear, but
you'd better ask the theoretical computing people for
a more competent rundown than I could give.
LH


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