Search Results for ""

Define g(k) as the quantity appearing in Waring's problem, then Euler conjectured that g(k)=2^k+|_(3/2)^k_|-2, where |_x_| is the floor function.

The field of reals is the set of real numbers, which form a field. This field is commonly denoted R (doublestruck R).

A spectrum formed by the Lagrange numbers. The only ones less than three are the Lagrange numbers, but the last gaps end at Freiman's constant. Real numbers larger than ...

If algebraic integers alpha_1, ..., alpha_n are linearly independent over Q, then e^(alpha_1), ..., e^(alpha_n) are algebraically independent over Q. The ...

A Meeussen sequence is an increasing sequence of positive integers (m_1, m_2, ...) such that m_1=1, every nonnegative integer is the sum of a subset of the {m_i}, and each ...

The British word for "zero." It is often used to indicate 0 subscripts, so a_0 would be spoken as "a naught."

Let (A,<=) and (B,<=) be well ordered sets with ordinal numbers alpha and beta. Then alpha<beta iff A is order isomorphic to an initial segment of B (Dauben 1990, p. 199). ...

The notation Q^_ denotes the algebraic closure of the rational numbers Q. This is equivalent to the set of algebraic numbers, sometimes denoted A.

The doublestruck letter R denotes the field of real numbers.

A tournament sequence is an increasing sequence of positive integers (t_1, t_2, ...) such that t_1=1 and t_(i+1)<=2t_i. Cook and Kleber (2000) show that Meeussen sequences ...