The function does not have a limit at if and only if one of its coordinate functions does not have a limit at .

For the distance function we have if and only if .

The vectors and are orthogonal, if .

One has the relationship between the scalar product and the norm: .

If is a linear map, then .

Let be an event and denotes the relative frequency of during independent experiment. Then for any one has

The probability density function of the continuous uniform distribution is

• , if ,
• , if ,
• , if .

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

For the expected value we have

Let be a random variable with values ,, … and correspondent probabilities , , … If the series is absolute convergent, then the expected value is