Re: Amateur math, neat relation

From: David C. Ullrich (ullrich_at_math.okstate.edu)
Date: 09/12/04 

Date: Sun, 12 Sep 2004 09:36:52 -0500

On 12 Sep 2004 04:11:18 -0700, jstevh@msn.com (James Harris) wrote:

>jstevh@msn.com (James Harris) wrote in message news:<3c65f87.0409101658.4d1d020d@posting.google.com>...
>> [...]
>I think the story is getting more interesting as someone pointed out
>that you can get my relation using the trivial relation
>
>[x] + [x + 1/2] = [2x]
>
>in reals with x = N/2j, but how would you know to try?

uh, right. nobody could possibly figure out any of this
trivia without you to guide them.

>Check this out. It's also trivially true (still in reals) that
>
>[x] + [x + 1/k] = [2x], with k>1,

right. how do you -prove- that? [no help from the audience, please.]

>[...]
>
>I think what's interesting here is that mathematicians don't seem to
>have figured out that they could compress counting composites in this
>way!

i wouldn't know about that, but i'm -certain- that they have
not figured out that [x] + [x + 1/k] = [2x], with k>1. when
you show us the proof of -that- you're going to be famous.

>So now I actually still need a citation!!!
>
>After all [x] + [x + 1/2] = [2x] IS trivial, but it takes a deeper
>understanding to figure out that you can use that to get
>
>[N/p] - [N/2p] - 1 = [(N-p)/2p]
>
>which gives you that [(N-p)/2p] is the count of odd *composites* up to
>and including N that have p as a factor!
>
>That is, math is full of tools. Some people can use basic tools to
>give surprising and interesting answers but just because the tools are
>simple, does it make the work useless?
>
>Understand? Do any of you understand that just because you can derive
>something deep from simple tools that doesn't mean that the derived
>result is worthless?
>
>It's one thing to have a simple way to derive a relation. It's
>another to even know the relation exists to be derived!
>
>How about this? Go find a reference that talks about counting
>composites, like to count primes, using compressed forms in any math
>book out there in all of the world.
>
>Go see for yourself that simple does not necessarily mean easy.
>
>Or never learn. I think some of you think that math must mean really
>very complicated and so difficult to understand that few people in the
>world can get it so it must be good.
>
>That's not true. Math is a lot more than showing off to other people.
>
>It's far deeper. And if any of you love mathematics itself, versus
>needing to show off on sci.math, then you might listen.
>
>
>James Harris

************************

David C. Ullrich

sorry about the inelegant formatting - typing
one-handed for a few weeks...

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