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Math Help - Set Multiplication

  1. #1
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    Set Multiplication

    Im going over old material of mine and cant remember how to multiply simple sets together. The sets I am trying to multiply together are {1,2,3} x {4,5}. Any anwsers would be very useful. Thanks Jon
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    Senior Member TriKri's Avatar
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    Quote Originally Posted by jonnysteals View Post
    Im going over old material of mine and cant remember how to multiply simple sets together. The sets I am trying to multiply together are {1,2,3} x {4,5}. Any anwsers would be very useful. Thanks Jon
    I have never heard of set multiplication before. Maybe someone else at this forum has. Are you sure you didn't intend to do a form of matrix multiplication,

    \left(\begin{array}{c}1\\2\\3\end{array}\right)\ti  mes\left(\begin{array}{cc}4&5\end{array}\right)\ =\ \left(\begin{array}{cc}<br />
    4&5\\<br />
    8&10\\<br />
    12&15<br />
\end{array}\right)
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  3. #3
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    Quote Originally Posted by jonnysteals View Post
    trying to multiply together are {1,2,3} x {4,5}.
    Usually that notation is for ‘cross products (Cartesian Products)’.
    \left\{ {1,2,3} \right\} \times \left\{ {4,5} \right\} = \left\{ {\left( {1,4} \right),\left( {2,4} \right),\left( {3,4} \right),\left( {1,5} \right),\left( {2,5} \right),\left( {3,5} \right)} \right\}.
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  4. #4
    Senior Member TriKri's Avatar
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    Aha, all different combinations one from each set. I have to read more courses.
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  5. #5
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    Yea if I had to guess thats what I would have guessed but I figured Id ask the more knowledge people on these boards. Thanks Jon. You guys respond very quick; I'm Impressed!.
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  6. #6
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    Hello, Jon!

    The sets I am trying to multiply together are {1,2,3} x {4,5}.

    As I recall, set multiplication doesn't involve arithmetic, just pairing.

    \{1,2,3\} \times \{4,5\} \;=\;\{(1,4),\,(1,5),\,(2,4),\,(2,5),\,(3,4),\,(3,  5)\}


    You see, set multiplication can be performed with sets like:
    . . \{\text{shoes},\text{ ships},\text{ sealing wax}\} and \{\text{cabbages},\text{ kings}\}

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