# Question on the meaning of cartesian product

I don't understand what they mean by on set $$A$$ and the meaning of binary expansion of same length does the question mean cartesian product?

• A relation on a set $A$ is simply a subset of $A\times A$. Here it is the set of ordered pairs $\langle a,b\rangle\in A\times A$ such that when you write the integers $a$ and $b$ in binary notation, they have the same number of digits (bits). For instance, $5=101_{\text{two}}$ and $6=110_{\text{two}}$, so both binary expansions have $3$ digits, and $\langle 5,6\rangle\in R$. But $3=11_{\text{two}}$ has only $2$ digits in its binary expansion, so $\langle 2,5\rangle\notin R$. – Brian M. Scott May 19 at 20:41