identity element in a sentence

Examples

1. The identity element is represented by the empty set.
2. Such identity elements have been used both in establishing theory and in computations; see below.
3. Many also have identity elements and inverse elements.
4. A semigroup has an " associative " binary operation, but might not have an identity element.
5. A trivial torsor corresponds to the identity element.
6. There can be ambiguity when two cycles share an element that is not the identity element.
7. The additive identity element is of course zero.
8. Reflection groups are necessarily achiral ( except for the trivial group containing only the identity element ).
9. This defines a group in which the identity element is and the inverse of the element is.
10. The identity element for multiplication is 1.