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Cartesian Product

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(Π΄Π΅ΠΊΠ°Ρ€Ρ‚ΠΎΠ²ΠΎ ΠΏΡ€ΠΎΠΈΠ·Π²Π΄Π΅Π½ΠΈΠ΅)

Given sets and , the cartesian product of and , denoted and read as ” cross ” is the set of all ordered pairs , where and .

Examples:

The number of pairs is derived from multiplying the cardinality of the sets ().

Cartesian Plane (Π΄Π΅ΠΊΠ°Ρ€Ρ‚ΠΎΠ²Π° Ρ€Π°Π²Π½ΠΈΠ½Π°) To find all the points on the cartesian plane, do the cartesian product of .

Properties

  • Distributive: or

The cartesian product of two sets is also a relation.

Graph View