Re: limitation to induction on finite bounds

From: |-|erc (gotch_at_beauty.com)
Date: 07/14/04


Date: Wed, 14 Jul 2004 01:03:02 GMT


"Peter R. Douglass" <peterd@ccs.neu.edu> wrote in
> PRD > (Non-Occurence Introduction 1)
> PRD > En e N, if( finite(length(d)), n<= length(d))
> PRD > Ai,
> PRD > !digitsmatchupton(i, d, n)
> PRD > -> d does not occur in S
>
> PRD > Could you please state the rule Non-Occurence
> PRD > Introduction 1 as an English sentence?
>
> HERC > if there exists a number n less than or equal to the
> HERC > length of string d, and there is no set member that
> HERC > matches the digits of d from digit 1 up to digit n,
> HERC > then d does not occur in S.
>
> PRD > Is this a direct translation?
>
> HERC > yes
>
> PRD > The term "finite(length(d))" occurs in the symbolic
> PRD > version of the rule. It does not occur in the English
> PRD > version. What happened to the "finite(length(d))"?
> PRD > How was that translated?
>
> HERC > its a type check to make the mathematical statement
> HERC > parsable on computer, its superfluous for english
>
> Let us suppose that the "finite(length(d))" is superfluous in English.
>
> Could you provide a translation into English which includes
> the superfluous information?
>
> My understanding of the rule is inadequate. If you can't translate
> your rule into English in a way that I can recognize all the parts
> in the symbolic version, then you will need to provide me with
> sufficient rules to understand how you manipulate symbolic
> formulae, such as the rule above.
>

Sure

> HERC > if there exists a number n less than or equal to the
> HERC > length of string d, and there is no set member that
> HERC > matches the digits of d from digit 1 up to digit n,
> HERC > then d does not occur in S.

If there exists a number n, and in the case that string d is only finite
length then n is less than or equal to the length of string d, ..

Herc



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