The dimension of the coordinate space is , by the basis exhibited above. The dimension of the polynomial ring "F"["x"] introduced above is countably infinite, a basis is given by , , , A fortiori, the dimension of more general function spaces, such as the space of functions on some (bounded or unbounded) interval, is infinite. Under suitable regularity assumptions on the coefficients involved, the dimension of the solution space of a homogeneous ordinary differential equation equals the degree of the equation. For example, the solution space for the above equation is generated by . These two functions are linearly independent over , so the dimension of this space is two, as is the degree of the equation.