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The general curve of a system which is linearly dependent on a certain number of given irreducible curves will not have a singular point which is not fixed for all the curves ...

A quaternion with complex coefficients. The algebra of biquaternions is isomorphic to a full matrix ring over the complex number field (van der Waerden 1985).

The number of "prime" boxes is always finite, where a set of boxes is prime if it cannot be built up from one or more given configurations of boxes.

If the total group of the canonical series is divided into two parts, the difference between the number of points in each part and the double of the dimension of the complete ...

A necessary and sufficient condition for a sequence S_i to converge. The Cauchy criterion is satisfied when, for all epsilon>0, there is a fixed number N such that ...

The number of coincidences of a (nu,nu^') correspondence of value gamma on a curve of curve genus p is given by nu+nu^'+2pgamma.

A solitaire game played with cards. The chance of winning is 1/13, and the arithmetic mean of the number of cards turned up is 42.4.

Given an arithmetic series {a_1,a_1+d,a_1+2d,...}, the number d is called the common difference associated to the sequence.

Given a geometric sequence {a_1,a_1r,a_1r^2,...}, the number r is called the common ratio associated to the sequence.

A compact surface is a surface which is also a compact set. A compact surface has a triangulation with a finite number of triangles. The sphere and torus are compact.