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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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