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Topic: Simple analytical properties of n/d
Replies: 20   Last Post: Mar 11, 2013 11:01 PM

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William Elliot

Posts: 1,488
Registered: 1/8/12
Re: Simple analytical properties of n/d
Posted: Mar 3, 2013 10:22 PM
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On Sun, 3 Mar 2013, Ross A. Finlayson wrote:

> Survey: does anybody find that:
> lim_d->oo lim_n->d n/d = 1
>
> It's clear that it does, for all values of d e N.
>
> Then, as a function f = n/d from N to R[0,1], d e N, n <= d E N, is it
> not constant monotone increasing?


Is that f(d) = n/d or f(n) = n/d?
What's deN and dEN?

> If not increasing, how is lim_n->d n/d = 1?

lim(x->d) x/d = 1, because since f(x) = x/d is continuous,
lim(x->d) x/d = d/d = 1

For integer variables n, lim(n->d) f(n) is meaningless.
Give a definition for it. Wouldn't it be the same as f(d)?

> Answer: it is.

Only if n is a real variable.



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