The update algorithm for gradient descent is
$$\theta_j = \theta_j - \alpha \frac{\partial}{\partial \theta_j}J(\theta)$$
$ \frac{\partial}{\partial \theta_j}J(\theta)$ have the unit of cost per unit $\theta$ but $\theta_j$ have the unit of $\theta$ and constant $\alpha$ is dimentionless, why is it valid that we can use subtraction for two element with different units?