The Texas Journal of Science, February 1st, 2005
Abstract. -- Subtraction has always been considered secondary to the fundamental and primary operation of addition, in some measure because addition is associative while subtraction is not. This note shows how to obtain an abelian group with an addition like operation (Joyner 2002:70-72) beginning with a subtraction binary operation.
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Definition 1: An ordered pair (S, -), with S a non-empty set and - being a binary operation on S, is called a subtractive groupoid if (1.) (a - b) - (c - d) = (d - b) - (c - a) for all a, b, c, d in S and (2.) there exists an element 0 in S such tha...
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