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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 ring of integers of a number field K, denoted O_K, is the set of algebraic integers in K, which is a ring of dimension d over Z, where d is the extension degree of K over ...

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.

The sequence {F_n-1} is complete even if restricted to subsequences which contain no two consecutive terms, where F_n is a Fibonacci number.