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An nth-rank tensor in m-dimensional space is a mathematical object that has n indices and m^n components and obeys certain transformation rules. Each index of a tensor ranges ...

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

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 sequence {a_1,a_2,a_3,...} fulfils a given property eventually if it fulfils it from some point onward, or, more precisely, if the property is fulfilled by the subsequence ...

The mathematical golden rule states that, for any fraction, both numerator and denominator may be multiplied by the same number without changing the fraction's value.

The greatest dividing exponent gde(n,b) of a base b with respect to a number n is the largest integer value of k such that b^k|n, where b^k<=n. It is implemented as the ...

The largest unit fraction, 1/2. 1/2 is a rational number with terminating decimal expansion 0.5.

The operation of subtraction, i.e., a minus b. The operation is denoted a-b. The minus sign "-" is also used to denote a negative number, i.e., -x.

The unit fraction 1/4, also called one-fourth. 1/4 is a rational number with terminating decimal expansion 0.25.