From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: (majordomo@vger.kernel.org) by vger.kernel.org via listexpand id S265210AbUAESDz (ORCPT ); Mon, 5 Jan 2004 13:03:55 -0500 Received: (majordomo@vger.kernel.org) by vger.kernel.org id S265211AbUAESDy (ORCPT ); Mon, 5 Jan 2004 13:03:54 -0500 Received: from fw.osdl.org ([65.172.181.6]:34533 "EHLO mail.osdl.org") by vger.kernel.org with ESMTP id S265210AbUAESDw (ORCPT ); Mon, 5 Jan 2004 13:03:52 -0500 Date: Mon, 5 Jan 2004 10:03:39 -0800 (PST) From: Linus Torvalds To: Davide Libenzi cc: Vojtech Pavlik , Andries Brouwer , Daniel Jacobowitz , Rob Love , rob@landley.net, Pascal Schmidt , Linux Kernel Mailing List , Greg KH Subject: Re: udev and devfs - The final word In-Reply-To: Message-ID: References: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: linux-kernel-owner@vger.kernel.org X-Mailing-List: linux-kernel@vger.kernel.org On Mon, 5 Jan 2004, Davide Libenzi wrote: > > Vojtech, a spiral (in the math sense) won't work It's not a spiral in that sense - it's just that the pattern you get when walking the "dots" looks like a spiral. > Also, IIRC, fractions are enumerable because they're a mapping from two > enumerable spaces (integers): F = F(I1, I2) = I1 / I2. Which is exactly the thing that Vojtech is really talking about: the enumerable space of a _discrete_ two-dimensional shape, ie folding two enumerable spaces onto one. The negative values don't matter, since you can effectively enumerate both ways starting from zero (ie the full set of integers is not any less enumerable than the positive numbers are): 0, 1, -1, 2, -2, 3, -3, ... so it doesn't really matter if you only enumerate one quadrant (which is effectively the same thing as enumerating fractions) or all four quadrants. The "spiral" pattern for a two-dimensional enumeration ends up being something like (0,0) -> (1,0) -> (0,1) -> (-1,0) -> (0, -1) -> (1,-1) -> (2,0) -> ... (do it on a graph paper and it's obvious, the above is probably wrong since I'm trying to visualize it) Linus