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The set R union {infty}, obtained by adjoining one improper element to the set R of real numbers, is the set of projectively extended real numbers. Although notation is not ...

The set R union {+infty,-infty} obtained by adjoining two improper elements to the set R of real numbers is normally called the set of (affinely) extended real numbers. ...

A rational number is a number that can be expressed as a fraction p/q where p and q are integers and q!=0. A rational number p/q is said to have numerator p and denominator ...

The field of all rational and irrational numbers is called the real numbers, or simply the "reals," and denoted R. The set of real numbers is also called the continuum, ...

The real axis is the line in the complex plane corresponding to zero imaginary part, I[z]=0. Every real number corresponds to a unique point on the real axis.

The real part R[z] of a complex number z=x+iy is the real number not multiplying i, so R[x+iy]=x. In terms of z itself, R[z]=1/2(z+z^_), where z^_ is the complex conjugate of ...

The term "real line" has a number of different meanings in mathematics. Most commonly, "real line" is used to mean real axis, i.e., a line with a fixed scale so that every ...

A real matrix is a matrix whose elements consist entirely of real numbers. The set of m×n real matrices is sometimes denoted R^(m×n) (Zwillinger 1995, p. 116).

A vector whose elements are real numbers.

A function whose range is in the real numbers is said to be a real function, also called a real-valued function.