Re: Fun, weird, sad, cool

From: James Harris (jstevh_at_msn.com)
Date: 09/10/04 

Date: 10 Sep 2004 15:39:03 -0700

"The Last Danish Pastry" <clivet@gmail.com> wrote in message news:<2qdqs3Ftqef8U1@uni-berlin.de>...
> "James Harris" <jstevh@msn.com> wrote in message
> news:3c65f87.0409091836.56fa26d1@posting.google.com...
>
> > After showing the actual linkages from my work to stuff like
> > Legendre's Formula I had a sad fear that maybe, you know, like maybe
> > mathematicians never understood the recurrence relationship with the
> > phi function.
> >
> > After all, my dS(x,y) function is rather specifically the count of
> > composites up to and including x that have y as a factor that do not
> > have any prime less than y as a factor.
> >
> > And I showed how it connects to a difference between phi sieve
> > functions, so if mathematicians had understood that the difference had
> > some interesting features, wouldn't they have talked about it?
> >
> > Like that definition I gave above for dS(x,y) means that if y is not

> > prime then dS(x,y) = 0, which is why my prime counting function finds
> > primes on its own.
> >
> > And then it gets weirder as I gave the derivation, finally, for
> >
> > [N/p] - [N/2p] - 1 = [(N-p)/2p]
> >
> > with p an odd prime, where in general you have
> >
> > [N/k] - [N/2k] - 1 = [(N-k)/2k]
> >
> > with k a natural greater than 1.
> >
> > Such a simple relation methinks can't be new. I wonder...
>
> Back in the mists of time... well... six weeks ago...
> No Way was explaining something to you...
> http://tinylink.com/?2GoRBD5hlN
>
> No Way:
> "Yes, it's constantly combing two terms with:
> [(N+k)/(2*k)] = [N/k] - [N/(2*k)]"
>
> Harris:
> "How do you get that?"
>
> Harris:
> "I'd be interested in a proof of that relation.
>
> Note that for the relations I gave I proved [(N-4)/6] directly by the
> method I've posted, and then used it with my prime counting function
> to find the other formulas.
>
> So, not surprisingly, I'm curious about how you came up with your
> formula, as I doubt you used my prime counting function.
>
> That is, I'd like to see the proof of your formula:
>
> [(N+k)/(2*k)] = [N/k] - [N/(2*k)]"
>
>
> A couple of people pointed out that the proof was trivial.

But they never gave a valid proof.

That's an important point as I looked over what posters gave and none
that I saw were valid which isn't surprising as there's one way to
prove the relation as it follows from evey odd being a 2k+1 where k is
a natural.

That is the basis for the compression.

And now it's supposedly trivial but FIND A FREAKING MATH TEXT THAT HAS
THE RELATION IN IT!!!!

You people are like animals. You don't think, you react.

> Now, if we take No Way's formula and replace N by N-k we get...
>
> [N/(2*k)] = [N/k] - 1 - [(N-k)/(2*k)]
>
> which... good grief... is your formula!!

I *derived* my formula, which means that there's no doubt about it.

I wonder about you people as you post on sci.math like you care about
mathematics, but you keep falling all over yourselves on simple
things.

The anonymous poster saw a pattern and conjectured.

I PROVED.

There is a difference.

Now then, if you think you're smart or even have a modicum of math
ability give one of the supposed proofs of the relation besides my
own.

My guess is that you'll just bull*** rather than meet the challenge.
 
> Evidently No Way has used time travel to steal your formula and has then
> replaced N by N+k in order to try to cover his tracks. That is the only
> explanation.

Actually if you knew a damn thing about mathematics then you'd
understand the difference between conjecturing and proving.

The anonymous poster saw a pattern. He guessed.

I PROVED.

Now I think you're a stupid *** with pretensions of actually
knowing mathematics who thinks he's doing something by continually
harassing me in posts over YEARS when you can't even do BASIC
MATHEMATICS.

If you can then give a proof.

That's it. The most basic test in mathematics that goes beyond
bull*** and words and social idiocy.

Give a freaking proof you *** or shut the hell up finally.

James Harris