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Newsgroups: alt.algebra.help
From: William Elliot <ma...@panix.com>
Date: Mon, 25 Jun 2012 04:03:53 -0700
Local: Mon, Jun 25 2012 7:03 am
Subject: Re: Polishing up II
On Mon, 25 Jun 2012, Jack wrote:
f(x) strictly decreases to 1 as x -> oo.
> Once again I have got this issue of wanting to say two things in one (and > ideally I want to be able to reference the assertion, all in one), namely > that f(x)/g(x) is strictly decreasing and approaches 1. > Currently I am writing
I suppose. So when defining f(x) ~ r, don't be glib,
> 'f(x)/g(x) ~ 1, the quotient being strictly decreasing' spell it all out. f is a monotonically decreasing function with lim(x->oo) f(x) = r. > or
No, that's saying something different.
> 'lim_(x-->oo) f(x)/g(x) = 1 > with f(x)/g(x) >1'. > I don't know if this is the best phrasing; I have read that the notation I Yes, asymptotic and monotone are different.
> am using here is known as asymptotic notation but my functions are > monotonic -- the curves they produce are smooth. Any views? > Also, I have changed the sentence <<For x<y in mathbb{N}, [x,y] = {n n {n n > mathbb{N} : x <= n <= y}
> mathbb{N} : x <= n <= y} >> given to me by Paul, to <<all intervals are > be taken to be intervals of integers>>. I wonder whether this is OK, > given that Paul's version might be seen to be doing something more, > namely indicating that the square brackets denote endpoints. Is the > open/-closed-bounded notation using round and square brackets > respectively, sufficiently standard that I don't need to worry? is a typo and skip the TeX.
In Europe, they use ]a,b[ for (a,b).
When restriced to integers only
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