Null (mathematics)

Null (mathematics)
For other uses, see Null (disambiguation).

In mathematics, the word null (from German null, which is from Latin nullus, both meaning "zero", or "none")[1] 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.

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 mathematical mapping is said to be null potent (or nilpotent) if repeated application can map the whole domain into the null element.

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.

References

  1. ^ ""null"". The Oxford English Dictionary, Draft Revision March 2004. 2004. http://dictionary.oed.com. Retrieved 2007-04-05. 

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