Re: abundance of irrationals!)

imaginatorium@xxxxxxxxxxxxx said:
>
> aeo6 Tony Orlow wrote:
> > mueckenh@xxxxxxxxxxxxxxxxx said:
> > >
> > >
> > > Remember: Every set of even numbers contains numbers which are
> larger
> > > tan the cardinality of that set. This is valid for *every* set of
> > > finite numbers. There is no reasonable arguing claiming that this
> > > situation should change in case of an "infinite" set.
>
> Yes there is - it's the error contained in the "salient point" below.
>
> Also some
> > > elements of an infinite set of even numbers would necessarily
> surpass
> > > the cardinality.
> > Yes. The salient point is that the set size can never be LARGER than
> the
> > largest element.
>
> Absolutely! The set size can never be LARGER than the largest element.
> Shout it from the rooftops! If you can find the largest element, the
> set size cannot be larger. Great! Do we all agree now??
>
> Uh-huh. Problem. What happens when there is NO largest element? Then
> the set size cannot be larger than, er, um, well, come in Houston, we
> don't seem to have a largest element here.
>
> Brian Chandler
> http://imaginatorium.org
>
>
Brian I already responded to that, you fool. You claim an infinite set
containing only finite values. You claim the argument fails because there is no
largest element, but whatever it is, it's finite. Well, if all values in the
set are finite, then they are all less than infinite, so the set size cannot be
infinite. QED

You certainly draw a lot of conclusions about a set which you cannot enumerate.
--
Smiles,

Tony
.

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