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A mathematical operation operates on an operand - or on an argument.
It is invalid because the conclusion does not follow logically from the premise.
It can be. It can rely on logic, and logic is related to math. In making arguments, they can use a lot of mathematical elements, like establishing numbers to prove the argument they are making.
A range used as a math term means subtracting the highest value from the lowest value. the set of values that a given function can take as its argument varies.
PRINCIPAL ARGUMENT = ARGUMENT + 2nPI arg(Z) = Arg (Z) + 2nPI