1.Previous
3.Next

of a and b: we have a <= a + b and b <= a + b and if x is an element of A with a <= x and b <= x, then a + b <= x. Similarly, a₁ + ... + a_n is the least upper bound of the elements a₁, ..., a_n.

Multiplication and addition are monotonic: if a <= b, then
* a + x <= b + x,
* ax <= bx, and
* xa <= xb for all x in A.

Regarding the star operation, we have
* 0^* = 1 and 1^* =

1.Previous
3.Next