Definition of 0 has definitions from the field of mathematics 1 [ noun ] (mathematics) a mathematical element that when added to another number yields the same number Synonyms Used in print(Kenneth Hoffman and Ray Kunze, Linear Al...) If * * f is the operator induced on * * f by T , then evidently * * f , because by definition * * f is 0 on the subspace * * f . When * * f for each i , we shall have * * f , because the operator * * f will then be 0 on the range of * * f . Since N and N ' are both nilpotent and they commute , the operator * * f is nilpotent ; for , using the fact that N and N ' commute * * f and so when r is sufficiently large every term in this expression for * * f will be 0 . ( Actually , a nilpotent operator on an n-dimensional space must have its nth power 0 ; if we take * * f above , that will be large enough . Such an operator is obviously the zero operator ; for since it is nilpotent , the minimal polynomial for this operator is of the form * * f for some * * f ; but then since the operator is diagonalizable , the minimal polynomial cannot have a repeated root ; hence * * f and the minimal polynomial is simply x , which says the operator is 0 . Related terms 2 [ adjective ] indicating the absence of any or all units under consideration Synonyms Examples "a zero score" Used in print(Frederick Mosteller et al., Probability with...) A trained marksman shooting five rounds at a target , all under practically the same conditions , may hit the bull's-eye from 0 to 5 times . 0 time ? Each binomial trial of a binomial experiment produces either 0 or 1 success . Related terms * Similar Spelling To share this definition click "text" (Facebook, Twitter) or "link" (blog, mail) then paste text link