I know what is a cartesian product of sets, for example, $M= \{1,2\} , N = \{a,b\} $
$M \times N = {(1,a), (1,b), (2,a) , (2,b)}$
but what is the Cartesian product of two intervals? say,
$[-5,1] \times [-2,3]$
Cartesian Product of Interval
2
$\begingroup$
interval-arithmetic
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0It's the square defined by those intervals. $(-5,-2)$ is the lower left corner and $(1,3)$ the upper right. Set of ordered pairs, one from the first set, the other from the second set. Intervals are sets. – 2017-02-16
1 Answers
5
By definition it is the set of couple:
$$
\{(x,y)|x\in[-5,1]\land y\in[-2,3] \}
$$
so it the rectangle $EFGH$ in the figure.
