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More options Oct 24 2010, 3:40 pm
Newsgroups: sci.math
From: master1729 <tommy1...@gmail.com>
Date: Sun, 24 Oct 2010 15:40:47 EDT
Local: Sun, Oct 24 2010 3:40 pm
Subject: Re: the tommy1729 website
lwalke wrote :

> Of course, we notice that there are actually four
> possible combos
> of truth values for these two atomic formulas:

> 1) xey & xfy
> 2) xey & ~xfy
> 3) ~xey & xfy
> 4) ~xey & ~xfy>

remember that i said x = [x] or in words :

all sets contain themselves.

so the set of all sets that dont contain themselves is empty.

i didnt even need 3-valued logic.

my system is strong , even stronger then you suspected.

( unfortunately currently not strong enough ( afak ) to be used in advanced number theory ... well if that is even possible from basic set theory / mereology / logic ideas ... then again i have proof of RH , Andrica and Twins and a weak generalization of those 3 [ collatz , beal , abc and hardy-littlewood seem unattackable ! :( ] )

> At first I thought that tommy1729 would accept
> classical analysis, but
> his recent comments on Newton's infinitesimals
> suggest otherwise. But
> nonetheless, if the theory can axiomatize Newton's
> infinitesimals,
> then that would be some mathematics suitable for one
> of the sciences,
> namely physics (i.e., classical mechanics).

look

the derivative of a differentiable real to real f(x) is

lim h-> 0 [f(x+h) - f(x)] / h

= lim n-> 'oo' [f(x+1/n) - f(x)] * n

hence the infinitesimal h = lim n-> 'oo' 1/n

i write 'oo' to avoid confusion with lim n-> oo 1/n = 0.

since afterall an infinitesimal is not 0.

=> conclusion 1 : h = lim n-> 'oo' 1/n

secondly 1,2,3,... w , where w = 'oo'.

'oo' is often called potential infinity ( or unbounded )
whereas oo is called actual infinity.

that is a recurring theme amongst critics , but also it appears in calculus e.g. divergence at the boundary ( consider radius = 1 , map oo to 1 and 'oo' is then the edge of the interior. ) or irrationality ( a limiting infinite sum of fractions is rational for all partial sums ( 'oo' ) but yet represents an irrational ( oo terms ) )

=> conclusion 2 : w = 'oo' = lim n -> 'oo'  n

hence when we solve : w * h = 1

we reduce by replacement using conclusion 1 and 2 :

lim n-> 'oo'  n * lim n-> 'oo' 1/n = 1

=>  lim n -> 'oo'  n  *  1/n  =  1

which is trivially true since n / n = 1

this also avoids ordinals cardinals and set axioms !

and you dont need to read all of newton either !

and we have our infinitesimal measure.

Q.E.D.

> Another science that might benefit from TST is
> computer science. Some
> people believe that 3-valued logic might actually be
> computationally
> more efficient than standard 2-valued logic. A Google
> search for
> "ternary computing" reveals several links concerning
> the future use
> of quantum ternary computers.

im skeptical of the quantum part at the moment , but indeed i have discussed this at university with ' IT people ' and we agreed on many things ( most dont dare to publish about it though , not surprising since i consider even myself a partial skeptic ).

regards

tommy1729