The type of elements in this ordered ring.
The type of elements in this ordered ring.
An element in this ring.
An element in this ring.
Returns the multiplicative identity of this ordered ring.
Returns the multiplicative identity of this ordered ring.
Returns the additive identity of this ordered ring.
Returns the additive identity of this ordered ring.
A totally ordered abstract ring structure. Addition associates and commutes, and multiplication associates and distributes over addition. Addition and multiplication both have an identity element, and every element has an additive inverse. To the extent practicable, the following axioms should hold.
Axioms for addition:
this
, then their sum 𝑎 + 𝑏 is also an element inthis
.this
.this
.this
has an elementzero
such thatzero
+ 𝑎 == 𝑎 for every element 𝑎 inthis
.this
corresponds an element -𝑎 inthis
such that 𝑎 + (-𝑎) ==zero
.Axioms for multiplication:
this
, then their product 𝑎 * 𝑏 is also an element inthis
.this
.this
has an elementunit
!=zero
such thatunit
* 𝑎 == 𝑎 for every element 𝑎 inthis
.The distributive law:
this
.Order axioms:
this
.this
.this
.0.1
0.0