Re: infinity

David Kastrup wrote:
> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> writes:
> > It has the property of finiteness, as a member of the set, whether
> > specifying it causes a contradiction or not. Maintaining the
> > property of finiteness produces no such contradictions. For every
> > initial sequence of the naturals, there does exist a largest
> > element, which is equal to the set size.
>
> This is better than watching a drunken schizophrenic mudwrestling with
> herself.

At some points though it's almost painful to watch. I think tony has
pretty much ruled out any sort of technical career for himself (not
just math). Try to do a Google search on Tony Orlow. Now imagine you
need to hire someone to do anything more complicated then shoveling
dung.

> >> > non-existence doesn't make it infinite.
> >>
> >> Non-existence means it has no properties.
>
> > That's a non-productive way to look at it,
>
> Sure, but mathematics, in contrast to digestion, does not demand
> productivity. So it is not an objective to add fibre to one's diet in
> order to produce more feces in mathematics.

Well you could also think of it as having ALL properties. The
statment, "x is blah" is true vacuously, if x does not exist. Although
blah can be anything. Of course saying the "largest finite number is
finite" is one such thing. The problem is that saying "the set of
finite numbers is finite" is not the same thing as the set of finite
numbers exist and thus we cannot make vacuous statements about it.

Actually by this logic you could also rule out say irrational numbers.
Take the dedekind cuts, now if sup of a cut does not exist in Q, then
you can "assume it is rational" (even if it doesn't exist) by the
"productivity axiom" of tony. Thus all reals are rational. See I can
make cranky "proofs" too!

Jiri

.

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