Comment on near zero

• agamemnonymous@sh.itjust.works ⁨10⁩ ⁨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- = -∞

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  • Leate_Wonceslace@lemmy.dbzer0.com ⁨10⁩ ⁨months⁩ ago

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

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    • agamemnonymous@sh.itjust.works ⁨10⁩ ⁨months⁩ ago

      Yes, but it is infinitesimally close.

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    • Gladaed@feddit.de ⁨10⁩ ⁨months⁩ ago

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

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      • Leate_Wonceslace@lemmy.dbzer0.com ⁨10⁩ ⁨months⁩ ago

        You also can’t call something infinity

        Why do you think that?

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• barsoap@lemm.ee ⁨10⁩ ⁨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.

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  • Leate_Wonceslace@lemmy.dbzer0.com ⁨10⁩ ⁨months⁩ ago

    I’m not familiar with IEEE 754.

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    • barsoap@lemm.ee ⁨10⁩ ⁨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.

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      • Leate_Wonceslace@lemmy.dbzer0.com ⁨10⁩ ⁨months⁩ ago

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

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    • Gobbel2000@programming.dev ⁨10⁩ ⁨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.

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    • barsoap@lemm.ee ⁨10⁩ ⁨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.

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• Gladaed@feddit.de ⁨10⁩ ⁨months⁩ ago

  Math is more than just the set of all algebras.

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  • Leate_Wonceslace@lemmy.dbzer0.com ⁨10⁩ ⁨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.

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    • barsoap@lemm.ee ⁨10⁩ ⁨months⁩ ago

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

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