Integer (computer science) at least 32 bits on any computer. Programmers may also incorrectly assume that a pointer can be converted to an integer without loss of information, which may work on (some) 32-bit computers, but fail on 64-bit computers with 64-bit pointers and 32-bit integers. A "short integer" can represent a whole number that may take less storage, while having a smaller range, compared with a standard integer on the same machine. In C, it is denoted by short. It is required to be at least 16 bits, and is often smaller than a standard integer, but this is not required. A
Algebraic number may consider numbers "explicitly" defined in terms of polynomials, exponentials, and logarithms – this does not include all algebraic numbers, but does include some simple transcendental numbers such as or ln 2. An algebraic integer is an algebraic number that is a root of a polynomial with integer coefficients with leading coefficient 1 (a monic polynomial). Examples of algebraic integers are , and . Note, therefore, that the algebraic integers constitute a proper superset of the integers, as the latter are the roots of monic polynomials for all In this sense, algebraic integers are to algebraic numbers what integers are