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The ideal quotient (a:b) is an analog of division for ideals in a commutative ring R, (a:b)={x in R:xb subset a}. The ideal quotient is always another ideal. However, this ...

A sequence {x_n} is called an infinitive sequence if, for every i, x_n=i for infinitely many n. Write a(i,j) for the jth index n for which x_n=i. Then as i and j range ...

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 ...

Let E be a set of expressions representing real, single-valued partially defined functions of one real variable. Let E^* be the set of functions represented by expressions in ...

An irreducible fraction is a fraction p/q for which GCD(p,q)=1, i.e., p and q are relatively prime. For example, in the complex plane, (4+7i)/(2+i)=3+2i is reducible, while ...

A sequence {a_j} of positive integers is called an iteration sequence if there exists a strictly increasing sequence {s_k} of positive integers such that a_1=s_1>=2 and ...

Approximations to Khinchin's constant include K = -(ln85181832)/(tan8) (1) = 1/(29)sqrt(6065) (2) = 6-sqrt(ln59055) (3) = 18^(27/79), (4) which are correct to 9, 7, 6, and 5 ...

The inertial subranges of velocity power spectra for homogeneous turbulence exhibit a power law with exponent -5/3. This exponent (-5/3) is called the Kolmogorov constant by ...

Lagrange's continued fraction theorem, proved by Lagrange in 1770, states that any positive quadratic surd sqrt(a) has a regular continued fraction which is periodic after ...

As Gauss showed in 1812, the hyperbolic tangent can be written using a continued fraction as tanhx=x/(1+(x^2)/(3+(x^2)/(5+...))) (Wall 1948, p. 349; Olds 1963, p. 138).