Ordered ring

Examples include the integers, the rationals and the real numbers.

In analogy with the real numbers, we call an element c of an ordered ring R positive if 0 < c, and negative if c < 0.

The set of positive elements of an ordered ring R is often denoted by R+.

The integers are a discrete ordered ring, but the rational numbers are not.

For all a, b and c in R: The list below includes references to theorems formally verified by the IsarMathLib project.

The real numbers are an ordered ring which is also an ordered field . The integers , a subset of the real numbers, are an ordered ring that is not an ordered field.