# associative operation वाक्य

###### उदाहरण वाक्यमोबाइल

- The first difficulty occurs with associative operations like addition and multiplication.
- Each reducer has an identity element and an associative operation that combines two values.
- Overriding is an associative operation; it has the empty function as an identity element.
- Then " is an associative operation with identity element ( 0, 1 ).
- However, mathematicians agree on a particular order of evaluation for several common non-associative operations.
- This expression could also have been simply evaluated right to left, because addition is an associative operation.
- Associative operations are abundant in mathematics; in fact, many algebraic structures ( such as categories ) explicitly require their binary operations to be associative.
- In general, parentheses must be used to indicate the order of evaluation if a non-associative operation appears more than once in an expression.
- Since this holds true when performing addition and multiplication on any real numbers, it can be said that " addition and multiplication of real numbers are associative operations ".
- Well-known categories are denoted by a short capitalized word or abbreviation in bold or italics : examples include "'composition as the associative operation on arrows.
- In the example above, + is an associative operation, so the final result will be the same regardless of parenthesization, although the specific way in which it is calculated will be different.
- Since conjunction is a commutative and associative operation, the formal setting-up of sequent theory normally includes "'structural rules "'for rewriting the sequent ? accordingly-for example for deducing
- A finger tree gives amortized constant time access to the " fingers " ( leaves ) of the tree, where data is stored, and also stores in each internal node the result of applying some associative operation to its descendants.
- There are 18 inequivalent ways to define an associative operation on three elements : while there are, altogether, a total of 3 9 = 19683 different binary operations that can be defined, only 113 of these are associative, and many of these are isomorphic or antiisomorphic so that there are essentially only 18 possibilities.

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