
Re: Another AC anomaly?
Posted:
Dec 18, 2009 7:22 AM


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.
> So the notion of n > growing bigger, as one tends to the limit, is not embodied > here since n is 0,1,1,1,1... as one proceeds and is 0 in > the limiting case.
Yes, as in many cases: lim  S_n  is not necessarily equal to lim S_n, whatever the definition of set limit. The same holds for limsup and liminf.  dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/

