I have defined an operation for entanglement of two natural numbers.
It is: $a$ T $b$
Example part 1 of 3:
$$ 13 \\ 24 \ \ \ \ $$ $$1 * 4$$
Example part 2 of 3:
$$ 13\\ 24 $$ $$1 * 2 + 3 * 4$$
Example part 3 of 3:
$$ 13\\ \ \ \ \ 24 $$ $$3* 2$$
Sum all results:
$$ (1 * 4) + (1 * 2 + 3 * 4) + (3 * 2) = 4 + 2 + 12 + 6 = 24 $$
Example part 1 of 3:
$$ 24 \\ 13 \ \ \ \ $$ $$2 * 3$$
Example part 2 of 3:
$$ 24\\ 13 $$ $$2 * 1 + 4 * 3$$
Example part 3 of 3:
$$ 24\\ \ \ \ \ 13 $$ $$4* 1$$
Sum all results:
$$ (2 * 3) + (2 * 1 + 4 * 3) + (4 * 1) = 6 + 2 + 12 + 4 = 24 $$
How to prove that this operation is commutative ?
From example, it seems that it is, but have no idea how to prove it.
From example: $a$T$b$ = $b$T$a$, where $a = 13$ and $b = 24$