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Topic: A finite set of all naturals
Replies: 43   Last Post: Aug 25, 2013 4:38 PM

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 Shmuel (Seymour J.) Metz Posts: 3,473 Registered: 12/4/04
Re: A finite set of all naturals
Posted: Aug 23, 2013 10:55 AM

In <ghae19tt5it7c9phdr64quip03q2dmdl29@4ax.com>, on 08/23/2013
at 04:40 AM, quasi <quasi@null.set> said:

>With Nam's new definition of positive/negative, I think
>it's immediately provable (subject to some clarification as to what
>a formula is) that odd(x) is a negative formula.

>Let even(x) <-> Ey(x=2*y).

Let odd(x) <-> Ey(S(x=2*y)).

>Assuming Nam's definition of "formula" supports the claim that
>even(x) is a positive formula, then odd(x) must be a negative
>formula since odd(x) is equivalent to ~even(x).

However, even(x) is equivalent to ~odd(x), so even(x) must be a
negative formula.

You can exclude S, but then you're no longer talking about the natural
numbers.

--
Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>

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Date Subject Author
8/22/13 namducnguyen
8/22/13 namducnguyen
8/23/13 Peter Percival
8/23/13 quasi
8/23/13 Peter Percival
8/23/13 namducnguyen
8/23/13 Peter Percival
8/24/13 Peter Percival
8/24/13 namducnguyen
8/23/13 Shmuel (Seymour J.) Metz
8/23/13 namducnguyen
8/23/13 Peter Percival
8/23/13 namducnguyen
8/24/13 Peter Percival
8/24/13 namducnguyen
8/24/13 Peter Percival
8/24/13 Shmuel (Seymour J.) Metz
8/25/13 namducnguyen
8/25/13 Peter Percival
8/25/13 fom
8/25/13 Shmuel (Seymour J.) Metz
8/24/13 Shmuel (Seymour J.) Metz
8/24/13 Shmuel (Seymour J.) Metz
8/23/13 tommy1729_
8/23/13 Peter Percival
8/23/13 namducnguyen
8/23/13 Peter Percival
8/23/13 namducnguyen
8/24/13 Peter Percival
8/24/13 namducnguyen
8/24/13 Peter Percival
8/24/13 namducnguyen
8/24/13 Peter Percival
8/24/13 namducnguyen
8/24/13 Peter Percival
8/24/13 fom
8/24/13 Ben Bacarisse
8/24/13 namducnguyen
8/24/13 fom
8/24/13 Peter Percival
8/24/13 fom
8/25/13 Peter Percival
8/23/13 Shmuel (Seymour J.) Metz