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Set-builder Notation
In set theory and its applications to logic, mathematics, and computer science, set-builder notation is a mathematical notation for describing a set by enumerating its elements, or stating the properties that its members must satisfy. Defining sets by properties is also known as set comprehension, set abstraction or as defining a set's intension. Sets defined by enumeration A set can be described directly by enumerating all of its elements between curly brackets, as in the following two examples: * \ is the set containing the four numbers 3, 7, 15, and 31, and nothing else. * \=\ is the set containing , , and , and nothing else (there is no order among the elements of a set). This is sometimes called the "roster method" for specifying a set. When it is desired to denote a set that contains elements from a regular sequence, an ellipses notation may be employed, as shown in the next examples: * \ is the set of integers between 1 and 100 inclusive. * \ is the set of natura ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Even Integer
In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is a multiple of two, and odd if it is not.. For example, −4, 0, 82 are even because \begin -2 \cdot 2 &= -4 \\ 0 \cdot 2 &= 0 \\ 41 \cdot 2 &= 82 \end By contrast, −3, 5, 7, 21 are odd numbers. The above definition of parity applies only to integer numbers, hence it cannot be applied to numbers like 1/2 or 4.201. See the section "Higher mathematics" below for some extensions of the notion of parity to a larger class of "numbers" or in other more general settings. Even and odd numbers have opposite parities, e.g., 22 (even number) and 13 (odd number) have opposite parities. In particular, the parity of zero is even. Any two consecutive integers have opposite parity. A number (i.e., integer) expressed in the decimal numeral system is even or odd according to whether its last digit is even or odd. That is, if the last digit is 1, 3, 5, 7, or 9, then it is odd; otherwis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
