Re: limitation to induction on finite bounds

From: |-|erc (gotcha_at_beauty.com)
Date: 06/24/04 

Date: Thu, 24 Jun 2004 00:03:52 GMT

"Will Twentyman" <wtwentyman@read.my.sig> wrote
> My recommendation is that you leave all programming concepts at the door
> when you post to sci.logic.

Classic!

>
> I'll say it one more time. A list is not the same as the limit of the
> elements on the list. That is why we have the limit function/operator.

Is this induction valid?

<
<1>
>
the sequence <2> is not in the list
:: the list is missing a finite sequence of digits

<
<12>
<34>
>
the sequence <25> is not in the list
:: the list is missing a finite sequence of digits

<
<123>
<456>
<789>
>
the sequence <260> is not in the list (ignore recurring 9s)
:: the list is missing a finite sequence of digits

Case n
<
<xx..3>
<xx..6>
..
<xx..9>
>
the sequence <yy..0> (the mod_diag) is not in the list
:: the list is missing a finite sequence of digits

IMPLIES

Case n+1
<
<xx..3a>
<xx..6b>
..
<xx..9c>
<xx..0d>
>
the sequence <yy..0e> (the mod_diag) is not in the list
:: the list is missing a finite sequence of digits

THERFORE
<
<x>
<xx>
...
>
This list is missing a finite sequence of digits.

___________________________________________

Is this valid?

0
0.1
0.12
This sequence contains the diagonal, 0.12

0
0.3
This sequence contains the diagonal, 0.3

0
0.3
0.33
0.333
0.3333
0.33333
This sequence contains the diagonal, 0.33333

3
3.1
3.14
3.141
This sequence contains the diagonal, 3.141

0
0.3
0.33
0.333
..

This sequence contains the diagonal, 0.33..

Herc

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