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Re: Another AC anomaly?
Posted:
Dec 14, 2009 10:29 AM
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In article <k9mdnWn11pFIAbjWnZ2dnUVZ_uWdnZ2d@giganews.com> "K_h" <KHolmes@SX729.com> writes:
Let's see whether I do understand what you want: ... > The sensibility of a definition is the real issue. Applying > the so-called standard definitions to {n} leads to a > cockamamie limit which is at odds with the general notion of > a limit.
That is your opinion.
> For a better definition, first choose one of the > wikipedia definitions.
We better choose a definition that fits, let's take the definition for sets with discrete metric on the elements.
> If a sequence of sets, A_n, cannot > be expressed as {X_n}, for some sequence of sets X_n, then > lim(n-->oo)A_n is defined by the wikipedia limit.
So with that definition lim sup(n -> oo) {1/n} = {} (note: we use a discrete metric on the rational numbers).
> Otherwise > let L=lim(n-->oo)X_n be the specified wikipedia limit for > X_n. If L exists then: > > lim(n-->oo)A_n = lim(n-->oo){X_n} = {L} > > otherwise lim(n-->oo)A_n = lim(n-->oo){X_n} does not exist. > Under this definition lim(n-->oo){n}={N}
By what definition is it {N}? By what definition is: lim(n -> oo) n = N? -- dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/
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