A real number is a member of the field containing all rational
and irrational numbers. The set of real numbers
is also called the continuum, denoted .
The set of reals is called Reals
in the Wolfram Language, and a number
can be tested to see if it is a member
of the reals using the command Element[x, Reals], and expressions
that are real numbers have the Head
of Real.
The real numbers can be extended with the addition of the imaginary numberi, equal to .
Numbers of the form,
where and are both real, are called complex
numbers, which also form a field. Another extension
which includes both the real numbers and the infinite ordinal
numbers of Georg Cantor is the surreal numbers.
The historical database "Plouffe's Inverter" cataloged real numbers related
to mathematical constants and functions.
Almost all real numbers are lexicons, meaning that they do not obey probability laws such as the law of large numbers (Gruber 1991;
Calude and Zamfirescu 1998; Trott 2004, p. 69).
containing all rational
and irrational numbers. The set of real numbers
is also called the continuum, denoted 
.
The set of reals is called Reals
in the Wolfram Language, and a number
can be tested to see if it is a member
of the reals using the command Element[x, Reals], and expressions
that are real numbers have the Head
of Real.
.
Numbers of the form 
,
where 
and 
are both real, are called complex
numbers, which also form a field. Another extension
which includes both the real numbers and the infinite ordinal
numbers of Georg Cantor is the surreal numbers.
