Re: infinity ...


albstorz@xxxxxx wrote:
> David R Tribble wrote:
>
> >
> > Consider the set of reals in the interval [0,1], that is, the set
> > S = {x in R : 0 <= x <= 1}. The elements of this set cannot be
> > enumerated by the naturals (which is why it is called an "uncountably
> > infinite" set). But all sets have a size, so this set must have a
> > size that is not a natural number. It is meaningless (and just
> > plain false) to say this set "has no size" or "is not a set".
>
>
> I'm not shure if the reals build a set in spite of you and Cantor and
> others are shure.
> A set is defined by consisting of discrete, distinguishable, individual
> elements. Now tell me: what separates a point on a line from the very
> next point on the line to be discrete? What separates sqrt(2) from the
> very next real number to be discrete?
> If you look only on individual points, you may have a set. But if you
> look on all of them?
>
> So, your above argumentation has no relevance to me. Proof the reals to
> be a set, then let's talk again.

What is your difficulty with the standard definitions?

Certainly the Integers { ... -3,-2,-1,0,1,2,3 ... }
form a set

Take the set of all pairs of integers (i,j) where
the second integer is not 0.

Take some equivalence classes of the above and we
have the rationals. (Note the rationals are not
discrete).

Take paris of sets of rationals (A,B) where all
the rationals in A are less than those in B and
where A union B is all the rationals. Now
we have the reals.

At which step do we fail to have a set?

-William Hughes

.

Relevant Pages

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