Null (mathematics)

Empty set symbols

In mathematics, the word null (from German: null meaning "zero", which is from Latin: nullus meaning "none")[1][2] 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 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. Retrieved 2007-04-05.
  2. ↑ "Definition of "null" adjective from the Oxford Advanced Learner's Dictionary". Oxford Advanced Learner's Dictionary 9th. 2016. Retrieved 2018-06-21.
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