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" ... Certain mathematical operations, like addition or multiplication, are order-independent, which means ... [+] they are commutative. If order does matter, and you get a result that's different depending on the order in which you perform your operations, those operations are non-commutative. This has key implications for the world of physics. ... "
" ... Why so many? This is where things get interesting. In most of the conventional mathematics we use, including most of the mathematics we use to model simple physical systems, all the operations are what we call commutative. Simply put, commutative means it doesn't matter what order you do your operations in. 2 + 3 is the same as 3 + 2, and 5 * 8 is the same as 8 * 5; both are commutative. ... "