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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: 1,226
Registered: 1/8/12
Re: Simple analytical properties of n/d
Posted: Mar 6, 2013 3:22 AM
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So far, skipping the stuff for the undefined f,
we have the definition f_d:R -> R, x -> x/d for d /= 0.

> But, the "area" under f_oo(n) = 1.

You haven't defined f_oo

> Consider lim_d->oo Int_0->d 1/d dx, that equals one.

lim(d->oo) integeral(0,d) 1/d dx = lim(d->oo) x/d|_0^d = 1

> This looks like a flat line infinitesimally greater than zero, the area
> under which sums to one.


Meaningless.

> So, there are some _interesting_ properties, of f_d(n) = n/d.

Exercise. Graph f:(R^2 - Rx{0}) -> R, (x,y) -> x/y.



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