lwalke wrote :
> Of course, we notice that there are actually fourremember that i said x = [x] or in words :
> possible combos
> of truth values for these two atomic formulas:
> 1) xey & xfy
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 acceptlook
> classical analysis, but
> his recent comments on Newton's infinitesimals
> suggest otherwise. But
> nonetheless, if the theory can axiomatize Newton's
> then that would be some mathematics suitable for one
> of the sciences,
> namely physics (i.e., classical mechanics).
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 )
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.
yes , glad you noticed.
> Another science that might benefit from TST is
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 ).
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