Prev: References added to Theology & Science: The Bible Is Scientific
Next: Countable ordinals
From: |-|ercules on 8 Jul 2010 02:42
"Transfer Principle" <lwalke3(a)lausd.net> wrote
> In standard theory, step (4) is invalid. In standard theory,
> it's possible that Chapernowne's constant contains every
> finite prefix of pi, yet not contain pi itself, just as it
> is possible for a list to contain every finite prefix of pi
> and not contain pi itself.


Step 4 is what I actually DISPROVE. I just took some liberty in the notation.

x = the number of digits in the expansion of C10
y = the number of consecutive digits of PI in C10

As x->oo, y->oo
x = oo

Assume the limit exists.
y=oo
Contradiction (for each finite starting digit of PI in C10 there is a finite ending digit)
Limit doesn't exist.

y cannot reach infinity
therefore x cannot reach infinity

this holds for x = any real without PI as a suffix
a similar proof searching for consecutive digits of e will hold for those exceptions having PI as a suffix

therefore no real number has an infinitely long expansion.

x = the number of digits in the expansion of C10
x =/= oo

Herc
From: |-|ercules on 8 Jul 2010 02:56
"|-|ercules" <radgray123(a)yahoo.com> wrote
> this holds for x = any real without PI as a suffix
> a similar proof searching for consecutive digits of e will hold for those exceptions having PI as a suffix

That might not be right!
PI segments aren't in all reals.

Herc
From: glird on 8 Jul 2010 17:04
On Jul 7, 9:30 am, Frederick Williams
>
>
>
>
> I can't go on, I'll go on.
>

You DO go on and on and on; but WHY?
First  |  Prev  | 
Pages: 1 2 3 4
Prev: References added to Theology & Science: The Bible Is Scientific
Next: Countable ordinals