In mathematics, a binary operation on a set is a calculation involving two elements of the set (called operands) and producing another element of the set (more formally, an operation whose arity is two). Examples include the familiar elementary arithmetic operations of addition, subtraction, multiplication and division. Other examples are readily found in different areas of mathematics, for example, vector addition, matrix multiplication and conjugation in groups.
Read more about Binary Operation: Terminology, Properties and Examples, Notation, Pair and Tuple, Binary Operations As Ternary Relations, External Binary Operations
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“An absolute can only be given in an intuition, while all the rest has to do with analysis. We call intuition here the sympathy by which one is transported into the interior of an object in order to coincide with what there is unique and consequently inexpressible in it. Analysis, on the contrary, is the operation which reduces the object to elements already known.”
—Henri Bergson (1859–1941)