this post was submitted on 18 May 2024
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Science Memes

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submitted 5 months ago by [email protected] to c/[email protected]
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[–] [email protected] 4 points 5 months ago (3 children)

What algebra uses negative 0?

[–] [email protected] 2 points 5 months ago (1 children)

Math is more than just the set of all algebras.

[–] [email protected] 2 points 5 months ago* (last edited 5 months ago) (1 children)

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.

Edit: I've given it some thought, and I'm not convinced all algebras can fit in a set, because every non-empty set can have at least one algebra imposed upon them, and so the set of all algebras must have cardinality no less than the proper class of all sets. We also can't have a set of all algebras (up to isomorphism) because iirc the surreal numbers are an algebra imposed on a structure that itself incorporates a proper class, and is thus incapable of being a set element.

[–] [email protected] 1 points 5 months ago

Depends, I'd say. Is your set theory incomplete or inconsistent?

[–] [email protected] 7 points 5 months ago (1 children)

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.

[–] [email protected] 1 points 5 months ago* (last edited 5 months ago) (3 children)

I'm not familiar with IEEE 754.

Edit: I think this sort of space shouldn't be the kind where people get downvoted for admitting ignorance honestly, but maybe that's just me.

[–] [email protected] 2 points 5 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.

[–] [email protected] 4 points 5 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.

[–] [email protected] 5 points 5 months ago* (last edited 5 months ago) (1 children)

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.

Mostly it's pure numerology, at least from the POV of most of the people using it.

[–] [email protected] 2 points 5 months ago

I'll need to look at it more; it sounds interesting.

[–] [email protected] 13 points 5 months ago (1 children)

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- = -∞

[–] [email protected] 16 points 5 months ago (2 children)

Speaking as a mathematician, it's not really accurate to call that -0.

[–] [email protected] 1 points 5 months ago (1 children)

You also can't call something infinity. People call stuff names. It is just important that they define their terms well enough.

[–] [email protected] 1 points 5 months ago

You also can't call something infinity

Why do you think that?

[–] [email protected] 5 points 5 months ago

Yes, but it is infinitesimally close.