Division? It's an Illusion: Division Does Not Exist.

What causes war and conflict between countries? The illusion of division aka separation. Division does indeed NOT exist! We have fooled ourselves alright. The illusion of division is the cause of most if not all problems in this world. Let's approach this not from the philosophical point of view but through simple mathematics.

When we do ordinary arithmetic, we are almost certainly working in a field. A field is just a set of numbers where we can do all "ordinary" addition, subtraction, multiplication, and division. But in the formal definition of a field, there are only two arithmetic operations: addition and multiplication.

So why is there no division? Because in a field, for any element

š‘„ š‘„ , we are guaranteed that two other elements exist:
The additive inverse
−š‘„ −š‘„ , where
š‘„+−š‘„=−š‘„+š‘„=0 š‘„+−š‘„=−š‘„+š‘„=0 ;
and the multiplicative inverse
1/š‘„ 1/š‘„ , where
š‘„×1/š‘„=1/š‘„ך‘„=1 š‘„×1/š‘„=1/š‘„ך‘„=1 (except for š‘„=0 š‘„=0 of course).

And so in a field, subtraction and division can be defined in terms of addition and multiplication, respectively, the latter of which are both commutative. So subtraction is not commutative, but additive inverses are commutative, and similarly for division and multiplicative inverses.