What algebra uses negative 0?
Comment on near zero
Gladaed@feddit.de 6 months agoAlso in Math.
Leate_Wonceslace@lemmy.dbzer0.com 6 months ago
agamemnonymous@sh.itjust.works 6 months 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 6 months ago
Speaking as a mathematician, it’s not really accurate to call that -0.
agamemnonymous@sh.itjust.works 6 months ago
Yes, but it is infinitesimally close.
Gladaed@feddit.de 6 months 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 6 months 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 6 months ago
I’m not familiar with IEEE 754.
barsoap@lemm.ee 6 months 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 6 months 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 6 months 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 6 months ago
Math is more than just the set of all algebras.
Leate_Wonceslace@lemmy.dbzer0.com 6 months 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 6 months ago
Depends, I’d say. Is your set theory incomplete or inconsistent?
marcos@lemmy.world 6 months ago
Unknowingly from the GP, that’s where CE got it from.
Gladaed@feddit.de 6 months ago
What is gp/ce?
marcos@lemmy.world 6 months ago
Grand parent / computer engineering