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For a sequence {a_n}, if a_(n+1)-a_n>0 for n>=x, then a_n is increasing for n>=x. Conversely, if a_(n+1)-a_n<0 for n>=x, then a_n is decreasing for n>=x. If a_n>0 and ...

An asymptotic series is a series expansion of a function in a variable x which may converge or diverge (Erdélyi 1987, p. 1), but whose partial sums can be made an arbitrarily ...

The terms of equational logic are built up from variables and constants using function symbols (or operations). Identities (equalities) of the form s=t, (1) where s and t are ...

The angular distance traveled around a circle is the number of radians the path subtends, theta=l/(2pir)2pi=l/r.

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 ...

The series producing Brun's constant converges even if there are an infinite number of twin primes, first proved by Brun (1919).

A number n satisfies the Carmichael condition iff (p-1)|(n/p-1) for all prime divisors p of n. This is equivalent to the condition (p-1)|(n-1) for all prime divisors p of n.