identity element Synonyms

No Synonyms and anytonyms found

identity element Meaning

Wordnet

identity element (n)

an operator that leaves unchanged the element on which it operates

identity element Sentence Examples

1. In algebra, the identity element is a unique element that, when combined with another element of the same set, leaves that element unchanged.
2. The identity element for addition is zero, as adding zero to any number does not change its value.
3. In the multiplicative group of real numbers, the identity element is one, due to the fact that multiplying any number by one results in the same number.
4. The identity element plays a crucial role in algebraic structures, defining the concept of neutral elements that preserve the properties of the operation.
5. For matrices, the identity element is the identity matrix, a square matrix with ones on the diagonal and zeros elsewhere.
6. In group theory, finding the identity element is essential for determining the order and properties of a group.
7. The identity element for the symmetric group is the permutation that leaves all elements in their original positions.
8. The identity element of a Boolean algebra is the element that represents the always-true statement.
9. In probability theory, the identity element is the element that corresponds to an event that always occurs.
10. The identity element is a fundamental concept in mathematics, providing a foundational understanding of operations and their properties.

FAQs About the word identity element

What is the meaning of the word identity element

an operator that leaves unchanged the element on which it operates

What are the synonyms of the word identity element

No synonyms found.

What are the antonyms of the word identity element

No antonyms found.

What is the usage of word identity element

In algebra, the identity element is a unique element that, when combined with another element of the same set, leaves that element unchanged.

The identity element for addition is zero, as adding zero to any number does not change its value.

How to use the word identity element in a sentence?

In the multiplicative group of real numbers, the identity element is one, due to the fact that multiplying any number by one results in the same number.

The identity element plays a crucial role in algebraic structures, defining the concept of neutral elements that preserve the properties of the operation.