Integer

One of the numbers ..., $-2$, $-1$, 0, 1, 2, .... The Set of Integers forms a Ring which is denoted $\Bbb{Z}$. A given Integer $n$ may be Negative ($n\in\Bbb{Z}^-$), Nonnegative ($n\in\Bbb{Z}^*$), Zero ($n = 0$), or Positive ( $n\in\Bbb{Z}^+=\Bbb{N}$). The Ring $\Bbb{Z}$ has Cardinality of Aleph-0. The Generating Function for the Nonnegative Integers is

$$f(x)={1\over(1-x)^2}=x+2x^2+3x^3+4x^4+\ldots.$$

There are several symbols used to perform operations having to do with conversion between Real Numbers and integers. The symbol $\left\lfloor{x}\right\rfloor$ (``Floor $x$'') means ``the largest integer not greater than $x$,'' i.e., int(x) in computer parlance. The symbol $[x]$ means ``the nearest integer to $x$'' (Nint), i.e., nint(x) in computer parlance. The symbol $\left\lceil{x}\right\rceil$ (``Ceiling $x$'') means ``the smallest integer not smaller $x$,'' or -int(-x), where int(x) is the Integer Part of $x$.

See also Algebraic Integer, Almost Integer, Complex Number, Counting Number, Cyclotomic Integer, Eisenstein Integer, Gaussian Integer, N, Natural Number, Negative, Positive, Radical Integer, Real Number, Whole Number, Z, Z-, Z+, Z*, Zero