• agamemnonymous@sh.itjust.works
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          5 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- = -∞

        • barsoap@lemm.ee
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          5 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
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            5 months ago

            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.

            • barsoap@lemm.ee
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              5 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.

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

            • Gobbel2000@programming.dev
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              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.

            • barsoap@lemm.ee
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              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.

          • Leate_Wonceslace@lemmy.dbzer0.com
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            5 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.

            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.

            • barsoap@lemm.ee
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              5 months ago

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

    • HexesofVexes@lemmy.world
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      5 months ago

      And, as a mathematician who has been coding a library to create scaled geometric graphics for his paper, I hate -0.0.

      Seriously, I run every number where sign determines action through a function I call “fix_zero” just because tiny tiny rounding errors pile up in floats, even is numpy.