Date: Jan 12, 2013 8:14 PM
Subject: Re: Finitely definable reals.
On Jan 11, 7:16 pm, Zuhair <zaljo...@gmail.com> wrote:
> Lets say that a real r is finitely definable iff there is a predicate
> P that is describable by a Finitary formula that is uniquely satisfied
> by r.
> Formally speaking:
> r is finitely definable <-> Exist P for all y. (P(y) <-> y=r)
> where of course P(y) is a Finitary formula.
> Of course NOT all reals are finitely definable in the above manner.
> This is an obvious corollary of Cantor's arguments of uncountability
> of reals.
> Also it is obvious that we have only COUNTABLY many finitely definable
> Other kinds of reals can be "infinitely" definable, this can be
> achieved in a language that encounters infinitely long strings of
> symbols, and many known first order languages are of that sort and
> they are proven to be consistent and even supportive of a proof
MODUS PONENS would not be able to make a single deduction.
This is where Mathematics went to Fairy land.
*CONTINUOUS LOGIC* Ask FRED THE FAGGOT HERE!
Take the powerset of ANYTHING (even True/False formula)
and just like the POWERSET(N) makes the continuous REALS!
You get CONTINOUS LOGIC FORMULA! <<<< ???
If you can REASON about infinitary formula THEN you already have an
alternate finite representation for them.