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Number |
 | | A new number was invented, the square root of negative one, denoted by i, a symbol assigned to this new number by Leonhard Euler. |
 | | Sets of numbers that are not subsets of the complex numbers include the quaternions, invented by Sir William Rowan Hamilton, in which multiplication is not commutative, and the octonions, in which multiplication is not associative. |
 | | The arithmetical operations of numbers, such as addition, subtraction, multiplication and division, are generalized in the branch of mathematics called abstract algebra, the study of abstract number systems such as groups, rings and fields. |
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