Identity Element (Noun)
Meaning
An operator that leaves unchanged the element on which it operates; "the identity under numerical multiplication is 1".
Classification
Nouns denoting relations between people or things or ideas.
Examples
- The number zero is the additive identity element for the set of integers.
- In abstract algebra, an identity element is an element that leaves unchanged the other elements of the set when the group operation is applied to it.
- The set of non-zero integers with the operation of multiplication has 1 as its multiplicative identity element.
- This property is known as the multiplicative identity property and the number 1 is known as the multiplicative identity element or identity for short.
- An element e of a mathematical structure is said to be an identity element if for all x in the structure we have x e = e x = x, where the operation in question is always the same.