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Topic: Matheology § 191
Replies: 3   Last Post: Jan 12, 2013 6:15 PM

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Ben Bacarisse

Posts: 1,915
Registered: 7/4/07
Re: Matheology § 191
Posted: Jan 12, 2013 2:34 PM
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WM <mueckenh@rz.fh-augsburg.de> writes:

> On 12 Jan., 16:24, Ben Bacarisse <ben.use...@bsb.me.uk> wrote:
>> WM <mueck...@rz.fh-augsburg.de> writes:
>> > Matheology § 191
>> > The complete infinite Binary Tree can be constructed by first
>> > constructing all aleph_0 finite paths and then appending to each path
>> > all aleph_0 finiteley definable tails from 000... to 111...

>> >         0
>> >       1, 2
>> >   3, 4, 5, 6
>> > 7, ...

>> > This Binary Tree contains aleph_0 * aleph_0 = aleph_0 paths.
>> No, it contains aleph_0 * whatever the cardinality of the set of tails
>> is.  Talk about begging the question!

> A tail can be defined by a finite word *only*. Nobody can quote an
> infinite string digit by digit - although most mathematicians believe
> that instinctively when pondering about set theory (but never when
> doing analysis).

That's the part that was missing. Without it you were begging the
question because the set of paths and the set of tails are equinumerous.
With it, the argument about tails and finite paths is pointless -- it's
just padding around the same tired old claim. Of course, you need
padded arguments so that you can keep posting...


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