Re: Orlow cardinality question

Virgil said:
> In article <MPG.1d1b9b0c5dea7d6c989e09@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
>
>
> > > Who says that number of elements is the one universal measure of
> > > sets? That is something you just made up. You have to define
> > > "number of elements" before the question even makes sense.
>
> > Which term do you not understand, "number" or "element"?
>
> How do you, TO, define "number of elements" of a set?
> It is not that we do not understand in general, it is that we do not
> know what your understanding about that phrase is.
How about the integral of the density over the domain? Does that satisfy your
need for mathematical definition? There are several ways to state this, but
"number of elements" is the most basic, and the way we intuitively think about
sets. A set is a number of elements, members, units, or whatever.
>
>
>
> > > You can use induction to prove that all finite sets have a certain
> > > property. You cannot use it to prove that an all infinite sets
> > > have a certain property.
>
> > Induction is supposed to prove something true for all members of the
> > infinite set of naturals.
>
> Only those members that can be generated by adding one once to some
> other member. There is no provision in induction for anything other than
> one-at-a-time.
Yeah like the entire set of naturals. Adding one an infinite number of times is
the same as adding infinity once, even if done one-at-a-time. There is not
"time" involved" That is a figure of speech.
>

--
Smiles,

Tony
.

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