On Thu, Apr 29, 2010 at 12:55 AM, Quincey Morris <quinceymor...@earthlink.net> wrote: > On Apr 28, 2010, at 20:49, Michael Ash wrote: > >> Actually, while there are finite decimal numbers with no finite binary >> representation, the reverse is not true. Every binary number can be >> represented by a finite number of decimal digits. I believe this is >> because 2 is a factor of 10. To prove it to yourself, just take >> successive negative powers of two and notice how you never get a >> repeating decimal. The fractional part of a binary float is just a sum >> of various negative powers of two, and if the individual components >> are finite, the result must be as well. > > I'm pretty sure that what I said was 100% accurate this morning, but that the > fundamental mathematical laws of the universe have changed since then and now > I'm wrong. You're right.
Understandable. If only the universe would sit still for a moment, maybe I could finally get a handle on it. >>> Plus, you'd have to expect that encoding doubles would require, in the >>> worst case, at least 309 significant digits, which is a much longer string >>> than I want in my archive. >> >> I think you've flipped your math around somewhere here. > > Yup, I noticed earlier I'd gone overboard with this, and got myself mixed up > with the maximum exponent. > > Good thing I published a disclaimer earlier, or otherwise I've have to feel > embarrassed now. Hey, as consequences for bad math go, this is pretty light. Mike _______________________________________________ Cocoa-dev mailing list (Cocoa-dev@lists.apple.com) Please do not post admin requests or moderator comments to the list. Contact the moderators at cocoa-dev-admins(at)lists.apple.com Help/Unsubscribe/Update your Subscription: http://lists.apple.com/mailman/options/cocoa-dev/archive%40mail-archive.com This email sent to arch...@mail-archive.com
