Integer

One of the numbers ... ,,,, 0, 1, 2, ... The set of integers forms a loop of representation. The given integer can be negative (), non-negative (), zero (), positive (). There is no doubt that integer sets are called integers in the Wolfram language. Then you can use the command Element [x, Integers] to see if it is a member of an integer. If the Wolfram language has a function header Integer, the IntegerQ [x] command will return True

Integer values ​​are sometimes expressed as "integers" (not integer values), but this may lead to unnecessary confusion with integral calculations.

The basis of the integer ring is aleph 0. A nonnegative integer generation function

There are several symbols used to perform operations related to the conversion between real numbers. The symbol ("floor") means "the largest integer below," that is, int (x) in computer terms. The symbol indicates "nearest integer" (nearest integer function). In computer terms, this is nint (x). The symbol ("ceiling") means "the smallest integer greater than or equal to" or -int (-x). Where int (x) is an integer part.

German mathematician and logicologist Kronec strongly opposed studies on the infinite set of George Kantar and that arithmetic and analysis should be based on integers and that he can only say that "God created natural numbers" The summary of the idea. All others are human tasks "(Bell 1986, p. 477)

An integer forms the smallest ring containing the smallest group and a natural number. In algebraic number theory, integers are sometimes called rational integers to distinguish them from more general algebraic integers. In fact, (rational) integers are algebraic integers, rational numbers. The symbol Z can be annotated to represent a different set of different usage between different authors. Z +, Z +, Z> for positive integers, Z≥ for nonnegative integers and Z Non for non-zero integers. Some use Z * to represent nonzero integers, others use nonnegative integers or {-1, 1}. Furthermore, Zp is used to represent a set of integers of modulo p, that is, a congruence class of a set of integers, or a set of p-ary integers.

Where a is a nonnegative integer and n is an integer. For example, in binary integers, U1 (1) is an odd set. Ua (n) is the set of all p-ary integers whose difference from n has a p-ary absolute value less than p1-a. In that case, Zp is compression of Z under the derived topology (Z is not a compressed version of normal discrete topology). The relative topology of Z as a subset of Zp is called the p-ary topology on Z. The topology of Zp is the topology of Cantor set. For example, you can perform a one-to-one continuous mapping by mapping between a binary integer and a Cantor set represented by radix 3 to in in Z2. Here, the topology of Qp is the topology of the Cantor set minus any point. In particular, Zp is compact, but Qp is not; in the local area it is compact. Both Zp and Qp are perfect as distance space