Definitions from the Web
Commutative Property
Description:
The commutative property is a fundamental property in mathematics that applies to binary operations such as addition and multiplication. It states that the order of the numbers or elements being operated on does not affect the final result.
Senses and Usages:
- Mathematics: In mathematics, the commutative property is commonly used in operations like addition and multiplication. For example, in addition, it states that changing the order of adding two numbers does not change the sum. Similarly, in multiplication, the commutative property states that changing the order of multiplying two numbers does not change the product.
- Popular: Beyond mathematics, the commutative property is also used figuratively to describe situations where the order or sequence of actions or events does not affect the final outcome or result. This concept is often applicable in various fields, such as logic, computer science, and finance.
- Local: In some local contexts or communities, the term "commutative property" may also refer to specific conventions or customs particular to that region. These may include traditional practices, cultural norms, or events that have a unique significance within the community in question.
Sample Sentences:
- The commutative property of addition can be explained using the example of swapping the order of two numbers: 3 + 4 is equal to 4 + 3.
- The commutative property of multiplication allows us to switch the order of factors without changing the final product, for example, 2 x 5 is equal to 5 x 2.
- In logic, the commutative property is applicable to the logical OR operation, where the order of operands does not impact the truth value of the expression.
- Many programming languages utilize the commutative property for bitwise operations, enabling developers to rearrange the sequence of bits without affecting the outcome.
- In finance, certain financial instruments exhibit commutative properties, where the order of investments or cash flows does not alter the overall return or performance.
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