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.

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.

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.