The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: A finite set of all naturals
Replies: 7   Last Post: Aug 23, 2013 3:01 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Ben Bacarisse

Posts: 1,972
Registered: 7/4/07
Re: A finite set of all naturals
Posted: Aug 23, 2013 9:49 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

quasi <quasi@null.set> writes:

> Peter Percival wrote:
>>Nam Nguyen wrote:
>>> I certainly meant "odd(x) can _NOT_ be defined as a
>>> positive formula ...".

>>Prove it.

> 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).
> 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).

That does not match my reading of the new definition. It states that a
formula is positive if it can be written in a particular form. That
odd(x) can be written in at least one form that does not match the
requirements for positivity does not mean that it can't be.

My first counter example, odd(x) <-> Ey[Sx=2*y] seems to me to be to as
positive as Nam's version of even, but he's forgotten about that as far
as I can tell.


Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.