• namelivia@lemmy.worldEnglish
    58·
    3 months ago

    -3 id the hidden dark version character of the solution, like evil ryu or devil jin.

  • xkforce@lemmy.worldEnglish
    7·
    3 months ago

    The number of solutions/roots is equal to the highest power x is raised to (there are other forms with different rules and this applies to R and C not higher order systems)

    Some roots can be complex and some can be duplicates but when it comes to the real and complex roots, that rule generally holds.

    • Beetschnapps@lemmy.world
      English
      2·
      3 months ago

      To translate: As a child learning math this equates to “ignore math, the explanations don’t explain anything real, they only explain more math.“

      “The only explanation is more abstraction with no real world application as far as math class is concerned. Frankly, there’s more application to your own life experience if you focus on language and the arts.”

        • Beetschnapps@lemmy.world
          English
          1·
          2 months ago

          I was one of those students who asked how it would be used, the teachers didn’t do the whole real world application part, and I never needed to go past trig.

          I work with engineers and use math like any other human on the planet but really wish mathematics was taught differently to make it more interesting. You hear a PHD candidate talk about the hairy ball problem and the math is interesting. Math class never was.

      • Maalus@lemmy.worldEnglish
        5·
        3 months ago

        Or you were just shit at maths and don’t have any idea how useful it is because you avoid it like the plague.

  • bleistift2@feddit.deEnglish
    5·
    3 months ago

    This only ever got handed down to us as gospel. Is there a compelling reason why we should accept that (-3) × (-3) = 9?

    • notabot@lemm.eeEnglish
      20·
      3 months ago

      You can look at multiplication as a shorthand for repeated addition, so, for example:

      3x3=0 + 3 + 3 + 3 = 9

      In other words we have three lots of three. The zero will be handy later…

      Next consider:

      -3x3 = 0 + -3 + -3 + -3 = -9

      Here we have three lots of minus three. So what happens if we instead have minus three lots of three? Instead of adding the threes, we subtract them:

      3x-3 = 0 - 3 - 3 - 3 = -9

      Finally, what if we want minus three lots of minus three? Subtracting a negative number is the equivalent of adding the positive value:

      -3x-3 = 0 - -3 - -3 - -3 = 0 + 3 + 3 + 3 = 9

      Do let me know if some of that isn’t clear.

      • bleistift2@feddit.deEnglish
        9·
        3 months ago

        This was very clear. Now that I see it, I realize it’s the same reasoning why x^(-3) is 1/(x^3):

         2 × -3 = -6
 1 × -3 = -3
 0 × -3 =  0
-1 × -3 =  3

        Thank you!

      • affiliate@lemmy.world
        English
        1·
        3 months ago

        i think this is a really clean explanation of why (-3) * (-3) should equal 9. i wanted to point out that with a little more work, it’s possible to see why (-3) * (-3) must equal 9. and this is basically a consequence of the distributive law:

        0  = 0 * (-3)
   = (3 + -3) * (-3)
   = 3 * (-3) + (-3) * (-3)
   = -9 + (-3) * (-3).

        the first equality uses 0 * anything = 0. the second equality uses (3 + -3) = 0. the third equality uses the distribute law, and the fourth equality uses 3 * (-3) = -9, which was shown in the previous comment.

        so, by adding 9 to both sides, we get:

        9 = 9 - 9 + (-3) * (-3).

        in other words, 9 = (-3) * (-3). this basically says that if we want the distribute law to be true, then we need to have (-3) * (-3) = 9.

        it’s also worth mentioning that this is a specific instance of a proof that shows (-a) * (-b) = a * b is true for arbitrary rings. (a ring is basically a fancy name for a structure with addition and distribute multiplication.) so, any time you want to have any kind of multiplication that satisfies the distribute law, you need (-a) * (-b) = a * b.

        in particular, (-A) * (-B) = A * B is also true when A and B are matrices. and you can prove this using the same argument that was used above.