Welcome to Wikipedia! - Rainwarrior 18:06, 16 August 2006 (UTC)[reply]

Baccyak-- happy to hear you'll be working on the Opus Dei page. If you haven't found it, allow me to point you to my proposed rewrite of the page User:Alecmconroy/Opus Dei. It _might_ be sort of what you're describing-- by and large, it has the same content as the current page, but has been reorganized with an eye to improving the tone of the article. I've been trying to get it to replace the current page (in whole or in part), but haven't met with much success. One of these days, maybe I'll find the time to do a massive comment-solicitation and/or go to Arbitration (assuming of course that the page doesn't get fixed first.

Anyway, I hope you like my version of things and maybe it'll make your life easier. Welcome to the Opus Dei article. --Alecmconroy 18:08, 8 September 2006 (UTC)[reply]

Alec, thank you for the welcome. After a fast but complete read, I do think your Opus Dei article version is a significant improvement, and your perspective is indeed close to what I was envisioning. Let's take subsequent discussion to the article's main Talk page, and I may chime in on the Talk page of your version as I see fit; I did see a couple of improvement potentials, but I do not want to reinvent the wheel, only perfect it.  ;-) Thanks for your efforts there. Baccyak4H 19:13, 8 September 2006 (UTC)[reply]

Thanks for the vote of confidence. I too can see a lot of room for improvement in the proposed rewrite, but I figured if I tried to make too many changes at once-- changing the tone AND the content, then it might never get it adopted. Also-- if you have any suggestions for how to get the revision approved, short of going to ArbCom, I'd love to hear it. This whole Opus Dei article has been a somewhat frustrating experience, but I'd hate for all the time I've put into it come to nothing. --Alecmconroy 01:43, 11 September 2006 (UTC)[reply]

Hi there Baccyak4H. I edited your contribution to harmonic series, stating that the first two series were equal. You are correct in saying that the second series consists of powers of two, but the indices of these powers are not integral for most values of 'k', as I think you intended. Here's why the first two series are equal:

Krasnay 20:53, 18 September 2006 (UTC)[reply]

Thanks for bring this to my talk page rather than just reverting ad nauseum.

However, I stand by my original derivation. (Actually, it wasn't mine; I just cleaned up what was already there and made the markup look nice (IMO!).)

Your proposed second equality is incorrect (the first and third are OK). Simply put, the returned value of the ceiling function is always an integer. Indeed, the function is defined to return the smallest integer not less than its argument. So, in the second expression, the exponent

always returns an integer. Thus the summand of the second expression is

Your second equality, which I dispute, asserts that (ignoring the common reciprocation for a moment), for any integer from 1 to , that (from the third expression) itself equals (from the second expression)

.

but that is simply impossible for = 3, 5, 6, 7, 9, etc. (that is, not 2, 4, 8, 16, 32, 64, etc.), since those integers are not integral powers of 2.

Put another way, the second equality holds only for which are integral powers of 2. For all other , the summand of the third expression is greater than that of the second expression.

Baccyak4H 02:43, 19 September 2006 (UTC)[reply]

You're absolutely right. I apologise. I did not spot the '\lceil \rceil' which makes the indices integral. I gather it means 'least integer not less than'? Again, I am sorry. Krasnay 08:17, 20 September 2006 (UTC)[reply]