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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- Dec 6th 2006, 05:05 AMjonnystealsSet 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

- Dec 6th 2006, 05:57 AMTriKri
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,

$\displaystyle \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}

4&5\\

8&10\\

12&15

\end{array}\right)$ - Dec 6th 2006, 06:25 AMPlato
Usually that notation is for ‘cross products (Cartesian Products)’.

$\displaystyle \left\{ {1,2,3} \right\} \times \left\{ {4,5} \right\} = \left\{ {\left( {1,4} \right),\left( {2,4} \right),\left( {3,4} \right),\left( {1,5} \right),\left( {2,5} \right),\left( {3,5} \right)} \right\}.$ - Dec 6th 2006, 06:42 AMTriKri
Aha, all different combinations one from each set. I have to read more courses.

- Dec 6th 2006, 07:10 AMjonnysteals
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!.

- Dec 6th 2006, 07:16 AMSoroban
Hello, Jon!

Quote:

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.__

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

You see, set multiplication can be performed with sets like:

. . $\displaystyle \{\text{shoes},\text{ ships},\text{ sealing wax}\}$ and $\displaystyle \{\text{cabbages},\text{ kings}\}$