Example · High school
Terms
| Term | This example | Why |
|---|
| group |
✓ |
The rational numbers form a group under addition, because $0$ is an identity and $-q$ is the inverse of $q$.
|
| ring |
✓ |
The rational numbers, with addition and multiplication, form a ring, because they satisfy the usual rules of arithmetic, including the distributive law.
|
| field |
✓ |
The rational numbers, with addition and multiplication, form a field, because multiplication is commutative and every nonzero fraction $a/b$ has the inverse $b/a$.
|
Distinctions using this example
All examples · All distinctions · All definitions