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**x3bnm** We know that cartesian product of two sets $\displaystyle A = \{a,b,c\}$ and $\displaystyle B = \{d,e,f\}$ is:

$\displaystyle A \times B\ =\ \{(a,d),(a,e),(a,f),(b,d),(b,e),(b,f),(c,d),(c,e), (c,f)\}$

and

$\displaystyle m\ \mathbf{div}\ n\ =$ the integer quotient obtained when $\displaystyle m$ is divided by $\displaystyle n $

$\displaystyle a\ \mathbf{mod}\ b\ =$ the integer remainder obtained when $\displaystyle a$ is divided by $\displaystyle b $

I'm reading a Discrete math book and I am on Functions chapter. It has a line in it that says: "$\displaystyle \mathbf{mod}$ and $\displaystyle \mathbf{div}$ are really functions defined on Cartesian products of integers."

Can anyone kindly tell me when I use $\displaystyle \mathbf{mod}$ and $\displaystyle \mathbf{div}$ functions how is that they are really functions on Cartesian products of integers?