# Divisibility Is a property of binary operations that is satisfied if, for any pair of elements $a$ and $b$, there exists another pair $x$ and $y$ such that: $ \begin{align} a \circ x &= b \\ y \circ a &= b \end{align} $ If the operation is also [[Commutativity|commutative]], $x$ and $y$ are the same. You can think of this as the ability of the binary operation to completely traverse the A set (you can use the operation to go to any element from any other element). Divisibility is closely related to [[Invertibility]]. If an operation is divisible, and also has an [[Identity|Identity Element]], it is considered [[Invertibility|invertible]].