If at point  the directional derivative of the function in the direction   is positive, then the function increases as one moves from in the direction .

If the function is continuous at , then it is also differentiable at .

In the scalar product is defined as

The vectors and are orthogonal, if .

The distance function satisfies .

If , then is linear.

The cumulative density function of the normal distribution is

The hypergeometric distribution with parameters , , and is the discrete probability distribution with possible values and probabilities

The standard deviation of the random variable is

The standard deviation can be calculated as