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Math Lesson 16.1.3 - Cartesian Square
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Welcome to our Math lesson on Cartesian Square, this is the third lesson of our suite of math lessons covering the topic of Relation and Function, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
Cartesian Square
A Cartesian square is obtained when all elements of the same set A multiply each other. In symbols, we express the Cartesian square as A × A or A2 (hence the name Cartesian square). The Cartesian plane discussed in the previous lesson is actually a Cartesian square because the elements in each direction are numbers, i.e. they belong to the same set - the set of real numbers R. The particular of Cartesian square elements is that they have the same number of inputs and outputs, i.e. the total number of ordered pairs obtained is a complete square, i.e. 1, 4, 9, 16, 25 and so on. For example, the Cartesian square of set A = {1, 2, 4} has 9 elements, that is 9 ordered pairs. Indeed, A × A = A2 = {(1, 1), (1, 2), (1, 4), (2, 1), (2, 2), (2, 4), (4, 1), (4, 2), (4, 4)}.
The figure below shows the Cartesian square above in the Cartesian plane. Please, observe the square shape of the figure obtained by the ordered pairs shown in this plane.
You have reached the end of Math lesson 16.1.3 Cartesian Square. There are 9 lessons in this physics tutorial covering Relation and Function, you can access all the lessons from this tutorial below.
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