Re: Well Ordering the Reals

Tony Orlow <aeo6@xxxxxxxxxxx> writes:

> Daryl McCullough said:
>> Tony Orlow says...
>>
>> >Oh come on. That set has one element, not an infinite number. Do
>> >you know what "number of" means?
>>
>> Nobody knows what *you* mean by "number of elements". They know
>> what people *normally* mean, but you have explicitly rejected that
>> definition.
>
> You HAVE no definition for number of elements for infinite sets. You
> have cardinality instead, which is not a particular number of
> elements, but an equivalence class that ignores actual numbers.

It is an equivalence class, period. Numbers are not relative for
establishing order among sets. It turns out that they are a
convenient help with finite sets, though.

> I don't reject bijections. I just consider them insufficient in
> themselves to declare equal set size or number of elements.

You came up with no sensible objection, though.

> It's a different animal.

Different from what? You consider surjectability not a good measure
of relative set size. But what you have come up as a substitute is
mere handwaving and babbling. And however insufficient or
dissatisfactory you may consider surjectability as a measure of set
size, your handwaving and babbling is worth nothing at all.

There are no "actual numbers" describing the set size of the naturals.
You have to invent new numbers for that, and if you do that, you have
to define the exact meaning of those inventions with regard to sets.

--
David Kastrup, Kriemhildstr. 15, 44793 Bochum
.

Relevant Pages

  • Re: Well Ordering the Reals
    ... > the rationals or reals here. ... and an infinite number of rationals for every unit. ... >>> substitute is mere handwaving and babbling. ...
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  • Re: Well Ordering the Reals
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  • Re: Well Ordering the Reals
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  • Re: Two results of set geometry
    ... Tony Orlow wrote: ... especially when you have infinite sets that are ... David R Tribble wrote: ...
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  • Re: Well Ordering the Reals
    ... >> Tony Orlow wrote: ... >> because infinite sets can be bijected to proper subsets, ... Outside TOmatics, all set sizes are properly measured by cardinality. ... >> the main entertainment value of your posts: ...
    (sci.math)
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