NONASSOCIATIVE Meaning and
Definition
-
Nonassociative refers to a property or characteristic whereby a mathematical operation or relationship does not adhere to the associative property. The associative property states that for a given operation, the grouping of the elements being operated on does not affect the outcome. In other words, when applying the associative property to a set of elements, their arrangement within parentheses does not matter.
When an operation is nonassociative, the order in which elements are grouped together becomes crucial to determining the result. In nonassociative operations, rearranging the parentheses can yield different outcomes.
This concept is commonly encountered in algebra, where operations such as addition and multiplication are frequently associative. For example, in regular arithmetic, the equation (2 + 3) + 4 and 2 + (3 + 4) both yield the same sum of 9. However, in a nonassociative operation, such as the division of numbers, the arrangement of elements matters. For instance, (10 ÷ 2) ÷ 5 results in a quotient of 1, while 10 ÷ (2 ÷ 5) produces a quotient of 25.
Nonassociativity is observed in various mathematical structures, including alternative and nonalternative algebras. These structures provide examples of nonassociative operations, leading to a departure from the associative property and presenting distinct properties and characteristics for exploration and analysis.
Common Misspellings for NONASSOCIATIVE
- bonassociative
- monassociative
- jonassociative
- honassociative
- ninassociative
- nknassociative
- nlnassociative
- npnassociative
- n0nassociative
- n9nassociative
- nobassociative
- nomassociative
- nojassociative
- nohassociative
- nonzssociative
- nonsssociative
- nonwssociative
- nonqssociative
- nonaasociative
Infographic
Add the infographic to your website:
