ec2-3-129-211-87.us-east-2.compute.amazonaws.com | ToothyWiki | RecentChanges | Login | Webcomic In standard number theory, -0 == 0 == +0. And the limit as x -> infinity of 1/x is equal to the limit of -1/x.
My limits may be a little rusty, but aren't these limits (as originally written: see Revision 3) 1 and -1 respectively?
D'oh. You are of course right. The ones I first tried were 2^-x and -(2^-x), but those tend to 1 and -1 as well. Okay, amended again... --AC
However, in the IEEE mathematical model, a concept of MinusZero exists, and -0 != +0.
Not true. -0 == 0. It's a special case of the equality relation. --Mjb67
Really?? ...Oh, well. Okay, they missed a simple opportunity there, to make things even more silly and counterintuitive than they have done already. --AC
(PeterTaylor) What else do you consider silly and counterintuitive? BTW The only way to distinguish between the zeroes (other than looking at their binary representations) is to reciprocate them and look at the sign of the resulting infinity.
Thus the limit as x -> infinity of 1/x is +0, but the limit of -1/x is -0.
It becomes more relevant when you consider that IEEE has an Epsilon (the smallest representable positive nonzero number). Thus epsilon * epsilon == +0, but - epsilon * epsilon == -0.
Anyone want to post any actual useful applications of this?
Well, my car has an external temperature gauge (digital) that sometimes displays -0, does that count? - Kazuhiko
Interesting. I suppose ln(x) should be NaN for all x<0, so it seems reasonable... sortof... to have ln(-0) = NaN also. Since -0 is intended to represent -epsilon^2 and suchlike, I guess. Fair cop. --AC
Lets you detect which direction you underflowed from? Rjk
My multimeter sometimes displays -0 when it reckons something is negative but too small to quantify. -- Admiral
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MinusZero