In the book 'Introduction to Algorithms 3/e', I have found the following definition of Binary Search Tree property:
Let $x$ be a node in a binary search tree. If $y$ is a node in the left subtree of $x$, then $y.key \leq x.key$. If $y$ is a node in the right subtree of $x$, then $y.key \geq x.key$.
My confusion is that while implementing binary search trees we either consider that the keys of left-subtree of a node $x$ would be $\leq x.key$ or the keys of right-subtree of a node $x$ would be $\geq x.key$ but not both. That is we follow one of the two convention. But in the property they have included $=$ in both the cases. Where am I wrong?
I would appreciate any idea on this issue.