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> In all fields and rings, multiplication and addition are related by the distributive property. That's a necessary condition for "repeated addition" to work f

• dragontamer 6y ago
  pi(3 + 5) == 3pi + 5pi == (Pi + Pi + Pi) + (Pi + Pi + Pi + Pi + Pi) == 8-pi. Am I missing something here? -------- This "multiplication is repeated addition through the distributed property" thing works on freaking __matricies__. They don't even have to be numbers or even related. Pi * ([ 1 0 ; + [ 1 0 ; 0 1 ] 2 1 ]) Pi * [ 1 0 ; + Pi * [ 1 0 ; 0 1 ] 2 1 ] [ Pi 0 ; + [ Pi 0 ; 0 Pi ] 2Pi Pi ] [ 2Pi 0 ; 2Pi 2Pi ] You can even "break up" the two matricies into its component parts: Pi * ( 1 0 + 0 0 + 1 0 + 0 0 + 0 0 ) 0 0 0 1 0 0 2 0 0 1 And you'll still get the correct answer: multiplication is repeated addition. Even with matricies. Even with vectors. Even in Galois Fields. Even with rational numbers. Even with real numbers. Even with Complex numbers. This property holds through all forms of math that I'm aware of.
  • iio8999 6y ago
    I think the issue is more about: 3 * pi = pi + pi + pi but how do you represent the other distribution, where 3 is added together pi times?
    • dragontamer 6y ago
      Break-up pi in whatever means you think is reasonable. 3 * (3 + 0.1 + 0.04 + 0.001 + 0.0005...) Aka: 9.4245... You know, how we've been multiplying 3 * pi for our whole lives. We split pi up into an infinite sum of component numbers (3, 1, 4, 1, 5, 9, 2, 6...) and then combine them together by individually multiplying the parts (3 * 3 + 3 * 0.1 + 3 * 0.04...)
      • pdonis 6y ago
        > Break-up pi in whatever means you think is reasonable. You can't. Pi is irrational.
        • dragontamer 6y ago
          > You can't. Pi is irrational. You just need to break it up infinitely times. We usually call the sequence 31415926...
          • pdonis 6y ago
            > You just need to break it up infinitely times. I've responded to this elsewhere in the thread: I don't think adopting increasingly perverse interpretations of "repeated addition" as you try to include more and more numbers is a useful way to teach multiplication.
            • beaconstudios 6y ago
              what they described is identical to long multiplication. That's not perverse, it's how most people multiply numbers.
    • jimhefferon 6y ago
      You extend to the rationals in the natural way, and then use continuity to define what happens for irrationals. (Of course, in a discrete context that doesn't apply. But the article's author is a grade school teacher.)
  • pdonis 6y ago
    > Am I missing something here? Sorry, I should have said substitute b = pi or c = pi. Or see the sibling post by iio8999.
• Gibbon1 6y ago
  pi isn't a counting number like you teach to children.