Re: [OT] Re: Second largest

Kelsey Bjarnason wrote On 08/08/07 12:03,:
On Mon, 06 Aug 2007 14:46:14 -0400, Eric Sosman wrote:


Kelsey Bjarnason wrote On 08/06/07 13:31,:

[snips]

On Mon, 06 Aug 2007 10:36:04 -0400, Eric Sosman wrote:


I think you'd better re-examine this argument. One
million log N is larger than log N by an amount most people would find
significant. Yes, even (in fact, especially) for very large N ...


But it's proportional to N, it doesn't vary by log of N or by square of
N, it varies proportional to N. It's an O(N) algorithm, just an
expensive one.

log N doesn't vary as log N?


Err... we were discussing an O(N) algorithm. If I misread a subsequent
insertion of a log, that's hardly something to get all shocked about.

We were discussing Knuth's "misuse" of Big-O in

H_n = ln n + gamma + O(1/n)

.... and some of its possible simplifications

H_n = ln n + O(1)

H_n = O(log n)

I brought up the multiplicative factor of a million and
the additive constant of a million in connection with the
last of these, to point out that the successive versions
give less and less information. You responded that the
additive constant is irrelevant for sufficiently large n
(true) and that so was the coefficient (no, the importance
of the coefficient does not diminish with increasing n).

Perhaps our entire set-to has just been a confusion
about the subject matter, causing us to use the same words
with different referents. If so, I apologize for my heat,
and to atone for any offense I offer you ein Gift.

;-)

--
Eric.Sosman@xxxxxxx
.

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