K_h
Posts:
419
Registered:
4/12/07


Re: Another AC anomaly?
Posted:
Dec 18, 2009 8:10 PM


"Dik T. Winter" <Dik.Winter@cwi.nl> wrote in message news:KuuL11.56J@cwi.nl... > In article <SqSdnSUF1q8FobbWnZ2dnUVZ_uCdnZ2d@giganews.com> > "K_h" <KHolmes@SX729.com> writes: > ... > > With the second option > > we > > can restrict ourselves just to the wikipedia definitions > > and > > define the sets n by: > > > > n = 0 = {} > > n = 1 = {{}} > > n = 2 = {{{}}} > > ... > > > > Wikipedia gives liminf(n>oo) n = 0. > > Only when we use the definition of limit on sequences of > sets, not when we > use the definition of limit on sequences of numbers. You > have to distinguish > the two and clearly state which one you are using.
In ZF set theory numbers are defined by sets and in this case there is no difference:
0 = {} 1 = {{}} 2 = {{{}}} ...
If the natural numbers are defined by these sets then liminf(n>oo)n=0. But yes, on the real number line, the "naturals" are still defined by sets but limits on real numbers are not defined by limits on their associated sets.
k

