- #1

arsenal_51

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So let's say we have three numbers, 1 2 3 (in this order)

and we have a container for this numbers: C

_{123}

and we have some operations: O

_{12}, O

_{13}and O

_{23}

each of these operations act on those numbers changing their positions.

For example O

_{12}will change the position of the first and second elements.

So let's say: O

_{12}. C

_{123}will equal: C

_{213}

And if we want to find out what operations to use when we have the original Container and the target Container we can do it easily graphically.

For example:

Original: C

_{123}

Target: C

_{231}

This can be done graphically:

The point where the lines intercept represent the operation between those two numbers. And the order is important, since these operations are not commutable.

So that's the same as: O

_{12}. O

_{23}. C

_{123}= C

_{231}

One last example:

The container doesn't need to hold all of the numbers of the three number-space

Original: C

_{12}

Target: C

_{31}

Or: O

_{23}. O

_{12}. C

_{12}= C

_{31}

So graphically its easy to find out the operations of any N number-space.

But how do we express that in a mathematical general expression?