In advanced algebra, point set topology and other mathematics books, this symbol is always used, and R or R in number theory represents the set of real numbers in set theory.

The complex number of radius can be radius (Latin complex number) or the conventional English complex number radius. The typical abbreviation and mathematical variable name of radius is called R, and by extension, the diameter d is defined as twice the radius: d=2r.

Typical field

Rational number field (q,+,*), real number field (r,+,*), complex number field (c,+,*), continuous function field (r,+,), etc.

But the integer set z is not a domain, because 1/x is not an integer. (Integer set Z is a ring, more precisely an integer ring)

If F is a subring of F and has an inverse to any non-zero element, then F is a subdomain of F, and the subdomain is also a domain. Generally speaking, we all study subdomains under typical domains. Subdomain criterion: subring+any non-zero element has an inverse element.