Null (mathematics)
In mathematics, the word null is often associated with the concept of zero or the concept of nothing. It is used in varying context from "having zero members in a set" to "having a value of zero".
In a vector space, the null vector is the neutral element of vector addition; depending on the context, a null vector may also be a vector mapped to some null by a function under consideration. In set theory, the empty set, that is, the set with zero elements, denoted "" or "∅", may also be called null set. 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. For example, in linear algebra, the null space of a linear mapping, also known as kernel, is the set of vectors which map to the null vector under that mapping.
In statistics, a null hypothesis is a proposition that no effect or relationship exists between populations and phenomena. It is the hypothesis which is presumed true—unless statistical evidence indicates otherwise.
