
Re: A finite set of all naturals
Posted:
Aug 23, 2013 2:42 PM


On 23/08/2013 8:55 AM, Shmuel (Seymour J.) Metz wrote: > 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.
You seem to be confused on the issue, which is that _in the natural_ _numbers_ while even(x) can be positively expressed _with only_ '*' can the same be said of odd(x)?
The correct answer is "NO".
What is _your answer_ to this question?
  There is no remainder in the mathematics of infinity.
NYOGEN SENZAKI

