Blumenthal, Leonard M. Formerly, Department of Mathematics, University of Missouri, Columbia, Missouri.
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One of the four fundamental operations of arithmetic and algebra. The first printed use of the symbol − to denote subtraction is in Johann Widman's Behennde und hüpsche Rechnung, Leipzig, 1489. Subtraction is often regarded as an operation inverse to addition, that is, if a and b are numbers, the number a − b is defined as that number which added to b gives a. The more modern viewpoint eliminates subtraction completely by considering the number a − b as the sum of a and that number (denoted by −b) which added to b gives 0. The number symbolized by −b is called the inverse of b (with respect to addition). Every real number has a unique inverse (the number 0 is its own inverse) and so for each two numbers x, y the operation x + (−y) gives a number. Clearly,
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