The space of bounded linear operators mapping a Banach space X into itself is not only a Banach space but also a Banach algebra with multiplication defined as composition. This provides additional possibilities of manipulation with elements of the space of operators. In particular, we can use `power series’ of operators to construct inverses of other operators, and thus solve linear equations in X. We can also define exponential functions of bounded linear operators to solve differential equations in X. Again, all of this would be impossible, were we not working in a complete space.