Example · High school
Terms
| Term | This example | Why |
|---|
| group |
✓ |
The nonzero real numbers form a group under multiplication, because $1$ is an identity and $1/x$ is the inverse of $x$.
|
| ring |
✗ |
The nonzero real numbers, with multiplication, do not form a ring, because a ring needs an addition too, and the nonzero real numbers are not closed under addition: $1 + (-1) = 0$.
|
| field |
✗ |
The nonzero real numbers are not a field without $0$ because a field requires there is an additive identity.
|
Distinctions using this example
All examples · All distinctions · All definitions