Definitely a repost, but it fits the season

    • CodexArcanum@lemmy.dbzer0.comEnglish
      3·
      8 days ago

      That would be the symbol\operation called TRUE or TOP or “tautology” which is always true. They’re actually missing quite a few of the weirder ops, including implication and biconditional\iff\if-and-only-if. (Edit: Actually I think XNOR is also the biconditional. I guess pretend like I said “material implication” and “reverse implication”. Fricken booleans man!)

        • CodexArcanum@lemmy.dbzer0.comEnglish
          1·
          8 days ago

          I truly have no idea and wish I did, haha. It looks like a shorthand for which operation is being followed, maybe like a group theory thing, but I really don’t know.

      • NeatNit@discuss.tchncs.de
        0·
        8 days ago

        I never got why “implies” is called that. How does the phrase “A implies B” relate to the output’s truth table?

        I have my own “head canon” to remember it but I’ll share it later, want to hear someone else’s first.

        • stingpie@lemmy.world
          0·
          8 days ago

          I think ‘implies’ asks whether it’s possible that A causes B to be true. In other words, it is false if there is evidence that A does not cause B.

          So:

          If A is true and B is false, then the result is false, since A could not cause B to be true.

          If A and B are both true, then the result is true, since A could cause B.

          If A is false and B is true, then the result is true since A could or could not make B true (but another factor could also be making B true)

          If A and B are both false we don’t have any evidence about the relationship between A and B, so the result is true.

          I don’t know for sure, though. I’m not a mathematician.

          • NeatNit@discuss.tchncs.de
            1·
            8 days ago

            Yup, that’s my interpretation too. It just doesn’t sit well with all the other operators.

            All the others are phrased as direct questions about the values of A and B:

            • A AND B = “Are A and B both true?”
            • A OR B = “Are either A or B true, or both?”
            • A NAND B = “Is (A AND B) not true?”
            • A IMPLIES B = “Is it possible, hypothetically speaking, for it to be the case that A implies B, given the current actual values of A and B?”

            You see the issue?

            Edit: looking online, some people see it as: “If A is true, take the value of B.” A implies that you should take the value of B. But if A is false, you shouldn’t take the value of B, instead you should use the default value which is inexplicably defined to be true for this operation.

            This is slightly more satisfying but I still don’t like it. The implication (ha) that true is the default value for a boolean doesn’t sit right with me. I don’t even feel comfortable with a boolean having a default value, let alone it being true instead of false which would be more natural.

            Edit 2: fixed a brain fart for A NAND B

  • noride@lemmy.zip
    2·
    8 days ago

    Honestly, this meme just legit helped me understand some of the tools in my CAD software.