Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Mathelogy S 011
Replies: 51   Last Post: May 22, 2012 6:04 PM

 Messages: [ Previous | Next ]
 Jesse F. Hughes Posts: 9,776 Registered: 12/6/04
Re: Mathelogy S 011
Posted: May 19, 2012 7:31 AM

WM <mueckenh@rz.fh-augsburg.de> writes:

> On 19 Mai, 05:06, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
>> WM <mueck...@rz.fh-augsburg.de> writes:
>> > On 19 Mai, 00:12, William Hughes <wpihug...@gmail.com> wrote:
>> >> On May 18, 2:47 am, Virgil <vir...@ligriv.com> wrote:
>>
>> >> > In article

>>
>> >> > WM <mueck...@rz.fh-augsburg.de> wrote:
>> >> > > God knows a list of all natural numbers [*].
>>
>> >> > Anyone who uses a claimed "God" to justify his mathematics is far more
>> >> > priest than mathematician.
>> >> > --

>>
>> >> Well, the use of the term "God" is harmless. I often talk
>> >> about "God's Algorithm" to refer to a desirable but impractical
>> >> way to a result. No theism is implied.

>>
>> > But Cantor's finished infinity and list of all reals implies theism.
>>
>> Right.
>>
>> Sure it does.
>>
>> Tell you what. Let's change the subject ever so slightly. Let's talk

>
> ZFC: There are countably many rationals and uncountably many
> irrationals in (0, 1).
>
> Now cover every rational with an interval, namely the n-th rational
> q_n with an interval of measure 10^-n. Then you cover 1/9 (or less) of
> the unit interval with aleph_0 intervals. In the remaining 8/9 (or
> more) there are uncountably many irrationals. But every two
> irrationals have a rational between each other. That implies in the
> present example, they have even a finite interval between each other,
> because there are no rationals outside of intervals. So we have
> uncountably many irrationals separated by countably many rationals.

Well, so much for talking about theorems of ZFC, eh?

> Usually there is some blathering about "Cantor-dust" in the reply. But
> even elements of Cantor-dust must be separated by intervals around
> rational numbers.

Quite right. You've proved ZFC is inconsistent and them mean ol'
mathematicians ignore you. My, oh my!

--
"I told her that I loved her.
She said she loved me too.
Neither one was lying,
Yet it wasn't true." -- Del McCoury Band