An elementary number is one formalization of the concept of a

closed-form number In mathematics, a closed-form expression is a expression (mathematics), mathematical expression that uses a finite set, finite number of standard operations. It may contain Constant (mathematics), constants, Variable (mathematics), variables, c ...

. The elementary numbers form an

algebraically closed field In mathematics, a field is algebraically closed if every non-constant polynomial in (the univariate polynomial ring with coefficients in ) has a root in . Examples As an example, the field of real numbers is not algebraically closed, because ...

containing the roots of arbitrary equations using

field Field may refer to: Expanses of open ground * Field (agriculture), an area of land used for agricultural purposes * Airfield, an aerodrome that lacks the infrastructure of an airport * Battlefield * Lawn, an area of mowed grass * Meadow, a grass ...

operations,

exponentiation Exponentiation is a mathematical operation, written as , involving two numbers, the '' base'' and the ''exponent'' or ''power'' , and pronounced as " (raised) to the (power of) ". When is a positive integer, exponentiation corresponds to re ...

, and

logarithm In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number to the base is the exponent to which must be raised, to produce . For example, since , the ''logarithm base'' 10 o ...

s. The set of the elementary numbers is subdivided into the explicit elementary numbers and the implicit elementary numbers.

References

* * * * Algebraic number theory {{Numtheory-stub