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The identity element I (also denoted E, e, or 1) of a group or related mathematical structure S is the unique element such that Ia=aI=a for every element a in S. The symbol ...

Given F_1(x,y,z,u,v,w) = 0 (1) F_2(x,y,z,u,v,w) = 0 (2) F_3(x,y,z,u,v,w) = 0, (3) if the determinantof the Jacobian |JF(u,v,w)|=|(partial(F_1,F_2,F_3))/(partial(u,v,w))|!=0, ...

Two lengths are called incommensurate or incommensurable if their ratio cannot be expressed as a ratio of whole numbers. Irrational numbers and transcendental numbers are ...

A p-form alpha is indecomposable if it cannot be written as the wedge product of one-forms alpha=beta_1 ^ ... ^ beta_p. A p-form that can be written as such a product is ...

If sets E and F are independent, then so are E and F^', where F^' is the complement of F (i.e., the set of all possible outcomes not contained in F). Let union denote "or" ...

A set whose members index (label) members of another set. For example, in the set A= union _(k in K)A_k, the set K is an index set of the set A.

An inner product space is a vector space together with an inner product on it. If the inner product defines a complete metric, then the inner product space is called a ...

The triangle DeltaA^'B^'C^' formed by the points of pairwise intersection of the three intangents. It is not in perspective with DeltaABC. It has trilinear vertex matrix ...

Integer division is division in which the fractional part (remainder) is discarded is called integer division and is sometimes denoted \. Integer division can be defined as ...

Given a commutative unit ring R and an extension ring S, an element s of S is called integral over R if it is one of the roots of a monic polynomial with coefficients in R.