Definition

1. Adjective (Mathematics):

   • Commutative: Describing a property in mathematics where the order of two operands in an operation does not change the result. For example, in addition or multiplication, swapping the numbers yields the same sum or product.

2. Verb (Archaic/Literary):

   • To exchange / To interchange: To mutually give and receive; to swap or trade items, ideas, or positions.

Usage Examples

• Adjective:

  • Phép cộng có tính chất giao hoán. (Addition has the commutative property.)
  • Đại số giao hoán là một nhánh quan trọng của toán học. (Commutative algebra is an important branch of mathematics.)

• Verb:

  • Hai bên giao hoán quà tặng. (The two sides exchanged gifts.)

Advanced Usage

• "Tính giao hoán": Commutativity (the noun form of the property).
  • Tính giao hoán không áp dụng cho phép trừ. (Commutativity does not apply to subtraction.)

Variants and Related Words

• Sự giao hoán (n): Commutation; the act or process of exchanging or the state of being commutative.

Synonyms

• Commutative (for the mathematical property).
• Interchangeable (capable of being exchanged).
• Exchange (the verb action).

Related Terms (Mathematics)

• Phép cộng giao hoán: Commutative addition.
• Phép nhân giao hoán: Commutative multiplication.
• Nhóm giao hoán: Commutative group (Abelian group).

1. Exchange, interchange
2. Commute
   • Đại số giao hoán
     Commulative algebra