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Likewise, the following numbers are not integers: 5/10, the square root of -9, 8.75, and [[pi]]. However, in larger systems of [[algebraic numbers]], the squareroot of -9 is considered to be an integer, but not a <b>rational integer</b>.
Likewise, the following numbers are not integers: 5/10, the square root of -9, 8.75, and [[pi]]. However, in larger systems of [[algebraic numbers]], the squareroot of -9 is considered to be an integer, but not a <b>rational integer</b>.
==Generalizations==
The set of integers form what is called in [[abstract algebra]] a [[ring]]. A ring is a set equipped with operations + and x with the usual properties learned in high-school algebra ([[commutativity]], [[distributivity]], [[linearity]], and [[associativity]]), identities for both operations, and inversion ([[subtraction]]). Other objects such as [[matrix]]es, [[polynomial]]s, [[quaternion]]s, and [[algebraic integer]]s also form rings, and can therefore be viewed as generalizations of the integers.
[[category:mathematics]]
[[category:mathematics]]