Null (mathematics)

For other uses, see Null (disambiguation).

In mathematics, the word null (from German: null meaning "zero", which is from Latin: nullus meaning "none") means of or related to having zero members in a set or a value of zero. Sometimes the symbol ∅ is used to distinguish "null" from 0. $\aleph_0$ is sometimes called Aleph null.

In a normed vector space the null vector is the zero vector; in a seminormed vector space such as Minkowski space, null vectors are, in general, non-zero. In set theory, the null set is the set with zero elements; and in measure theory, a null set is a set with zero measure.

A null space of a mapping is the part of the domain that is mapped into the null element of the image (the inverse image of the null element).

In statistics, a null hypothesis is a proposition presumed true unless statistical evidence indicates otherwise.