Re: [PO] Re: Proving a negative is hard

From: David C. Ullrich (ullrich_at_math.okstate.edu)
Date: 08/22/04 

Date: Sun, 22 Aug 2004 06:07:09 -0500

On Sun, 22 Aug 2004 04:01:08 GMT, "Peter Olcott"
<olcott@worldnet.att.net> wrote:

>
>"Daryl McCullough" <daryl@atc-nycorp.com> wrote in message news:cg54720302i@drn.newsguy.com...
>> Peter Olcott says...
>>
>> >"Daryl McCullough" <daryl@atc-nycorp.com> wrote
>>
>> >> 1. Assume there is a program H(x,y) that returns true if
>> >> x is a code for a program that halts on input y, and returns
>> >> false otherwise.
>> >
>> >I would say that this is a false assumption.
>>
>> That's correct. It is provably false that there is a program
>> H(x,y) that returns true if x is a code for a program that halts
>> on input y, and returns false otherwise. Glad you agree.
>
>If you make this assumption then eliminating the undecidability
>of the Halting Problem is not possible. If you do not make this
>assumption the deciding whether or not each and every element
>of the set of all TM's is not undecidable. Whenever I make any
>assumptions, I try very hard not to make any arbitrary assumptions
>that block my path to a solution.

simply amazing, the fact that you accuse people of not understanding
basic logic and then -show- that you don't.

assumption 1 is the start of a proof by contradiction. we assume
1, we derive a contradiction, and we conclude that 1 is false.

i mean duh.

************************

David C. Ullrich

sorry about the inelegant formatting - typing
one-handed for a few weeks...

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