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In abstract algebra, there is a wide variety of operations: geometric transformations, function composition, matrix multiplication But many sets of elements have the familiar operations from arithmetic: addition, subtraction, multiplication and division. Loosely speaking, if you can add and subtract, you have a group. If you can add, subtract and multiply, you have a ring. But if youre lucky and get all four operations, the result is an object that behaves similarly to the numbers you learned about in arithmetic and algebra. We call these fields. One thing weve talked about before, but it bears repeating, is that in abstract algebra, subtraction is actually adding with negatives. For example, 3 minus 5 is the same as 3 plus negative 5. So instead of saying you can add and subtract, we say theres addition and additive inverses. Notice that word additive? Thats because there is more than one kind of inverse. For example, 3 DIVIDED by 5 is the same as 3 times 1/5. So ins