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COMMUTATIVITY This seems to be a very misunderstood concept of elementary mathematics which limits itself to stating that "addition and multiplication are commutative but subtraction and division are not". We are temped to believe that these statements are questionable and that another, far more relevant, remains unsuspected. False The habitual definition of commutativity runs something like this. "Addition is commutative because 2 + 3 = 3 + 2, but subtraction is not commutative because 2 - 3 /= 3 - 2". Multiplication and division are treated the same way. The problem here seems to be one
of misinterpreting the syntax of the mathematical symbols.
The "+" sign is interpreted as being a conjunction, like
the word "and", when in reality it is the imperative verb
"add" with complement 3, creating a phrase "to the value 2,
add the value 3".
The value 2 is not there by chance, but is the result of
"to the value 0, add the value 2", for a complete phrase
"to the value 0, add the value 2, then add the value 3".
This is evidently commutative with "to the value 0, add
the value 3, then add the value 2". Now if the same
procedure were applied to subtraction, we would have
"to the value 0, add the value 2, then subtract the value 3",
which would be perfectly commutative with
"to the value 0, subtract the value 3, then add the value 2".
True Lost in a jungle of misinterpreted
syntax, the veritable enigma of commutativity seems to have
been completely overlooked, and that is the commutativity of How come What is the basic difference between addition and multiplication |

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