What algebra uses negative 0?
Comment on near zero
Gladaed@feddit.de 1 month agoAlso in Math.
Leate_Wonceslace@lemmy.dbzer0.com 1 month ago
agamemnonymous@sh.itjust.works 1 month ago
When taking about limits, you can approach 0 from the positive or negative direction, which can give very different results. For example, lim cotx, x->0+ = ∞ while lim cotx, x->0- = -∞
Leate_Wonceslace@lemmy.dbzer0.com 1 month ago
Speaking as a mathematician, it’s not really accurate to call that -0.
agamemnonymous@sh.itjust.works 1 month ago
Yes, but it is infinitesimally close.
Gladaed@feddit.de 1 month ago
You also can’t call something infinity. People call stuff names. It is just important that they define their terms well enough.
barsoap@lemm.ee 1 month ago
IEEE 754
I mean it’s an algebra, isn’t it? And it definitely was mathematicians who came up with the thing. In the same way that artists didn’t come up with the CGI colour palette.
Leate_Wonceslace@lemmy.dbzer0.com 1 month ago
I’m not familiar with IEEE 754.
barsoap@lemm.ee 1 month ago
It’s a wonderful world where 1 / 0 is ∞ and 1 / -0 is -∞, making a lot of high school teachers very very mad. OTOH it’s also a very strange world where x = y does not imply 1 / x = 1 / y. But it is, very emphatically, an algebra.
Gobbel2000@programming.dev 1 month ago
IEEE 754 is the standard to which basically all computer systems implement floating point numbers. It specifically distinguishes between +0 and -0 among other weird quirks.
barsoap@lemm.ee 1 month ago
You probably are familiar with the thing, just not under that name, and not as a subject of mathematical study. I am aware that there are, at least in theory, mathematicians never expanding beyond pen+paper (and that’s fine) but TBH they’re getting kinda rare. The last time you fired up Julia you probably used them, R, possibly, Coq, it’d actually be a surprise.
They’re most widely known to trip up newbie programmers, causing excessive bug hunts and then a proud bug report stating “0.1 + 0.2 /= 0.3, that’s wrong”, to which the reply will be “nope, that’s exactly as the spec says”. The solution, to people who aren’t numerologists, is to sprinkle gratuitous amounts of epsilons everywhere.
Gladaed@feddit.de 1 month ago
Math is more than just the set of all algebras.
Leate_Wonceslace@lemmy.dbzer0.com 1 month ago
I’m aware. Algebra is what I’m most interested in, and so when someone says “0” I think “additive identity of a ring” unless context makes the use obvious.
barsoap@lemm.ee 1 month ago
Depends, I’d say. Is your set theory incomplete or inconsistent?
marcos@lemmy.world 1 month ago
Unknowingly from the GP, that’s where CE got it from.
Gladaed@feddit.de 1 month ago
What is gp/ce?
marcos@lemmy.world 1 month ago
Grand parent / computer engineering