Re: Well Ordering the Reals

In article <MPG.1dd3f49f4412860a98a637@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow <aeo6@xxxxxxxxxxx> wrote:

> Daryl McCullough said:
> > Tony Orlow says...
> > >
> > >imaginatorium@xxxxxxxxxxxxx said:
> >
> > >> Or are there really
> > >> more representations of numbers in C than there are numbers in C. Or it
> > >> the relation between "binary N" and whatever "N" is the size of C just
> > >> so as to make them match up after all?
> > >It depends whether you are interpeting the strings as quantities, or just
> > >as
> > >raw strings. See? You can give a reasonable answer, even if the question
> > >didn't
> > >expect it.
> >
> > So you *are* saying that whether set A is bigger than set B is a
> > *subjective* judgement; it depends on how you *interpret* the elements
> > of A?
> >
> > --
> > Daryl McCullough
> > Ithaca, NY
> >
> >
> I wouldn't say it is "subjective", but dependent on context.

Which makes it subjective.

In mathematics, a set is entirely determined by what objects are members
and what are non-members of that set. The context in which that set
occurs is irrelevant to the set's identity.

If two sets have the same members in any context then they are
identically equal sets in every context.
.

Relevant Pages

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