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A sequence of positive integers {a_n} such that sum1/(a_nb_n) is irrational for all integer sequences {b_n}. Erdős showed that {2^(2^n)}={1,2,4,16,256,...} (OEIS A001146) is ...

For any real number r>=0, an irrational number alpha can be approximated by infinitely many rational fractions p/q in such a way that ...

The decimal expansion of a number is its representation in base-10 (i.e., in the decimal system). In this system, each "decimal place" consists of a digit 0-9 arranged such ...

A plot of the map winding number W resulting from mode locking as a function of Omega for the circle map theta_(n+1)=theta_n+Omega-K/(2pi)sin(2pitheta_n) (1) with K=1. (Since ...

The Burnside problem originated with Burnside (1902), who wrote, "A still undecided point in the theory of discontinuous groups is whether the group order of a group may be ...

Exponentiation is the process of taking a quantity b (the base) to the power of another quantity e (the exponent). This operation most commonly denoted b^e. In TeX, the ...

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 ...

Given a Lyapunov characteristic exponent sigma_i, the corresponding Lyapunov characteristic number lambda_i is defined as lambda_i=e^(sigma_i). (1) For an n-dimensional ...

The odd part Od(n) of a positive integer n is defined by Od(n)=n/(2^(b(n))), where b(n) is the exponent of the exact power of 2 dividing n. Od(n) is therefore the product of ...

As of 2014, the IEEE 754-2008 is the most commonly implemented standard for floating-point arithmetic. This framework is a massive overhaul of its predecessor IEEE 754-1985 ...