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The unique nonnegative square root of a nonnegative real number. For example, the principal square root of 9 is 3, although both -3 and 3 are square roots of 9. The concept ...

A positive proper divisor is a positive divisor of a number n, excluding n itself. For example, 1, 2, and 3 are positive proper divisors of 6, but 6 itself is not. The number ...

The Q-chromatic polynomial, introduced by Birkhoff and Lewis (1946) and termed the "Q-chromial" by Bari (1974), is an alternate form of the chromatic polynomial pi(x) defined ...

The limiting rabbit sequence written as a binary fraction 0.1011010110110..._2 (OEIS A005614), where b_2 denotes a binary number (a number in base-2). The decimal value is ...

A radical integer is a number obtained by closing the integers under addition, multiplication, subtraction, and root extraction. An example of such a number is RadicalBox[7, ...

The nth Ramanujan prime is the smallest number R_n such that pi(x)-pi(x/2)>=n for all x>=R_n, where pi(x) is the prime counting function. In other words, there are at least n ...

The term "real line" has a number of different meanings in mathematics. Most commonly, "real line" is used to mean real axis, i.e., a line with a fixed scale so that every ...

The field of all rational and irrational numbers is called the real numbers, or simply the "reals," and denoted R. The set of real numbers is also called the continuum, ...

A prime which does not divide the class number h(p) of the cyclotomic field obtained by adjoining a primitive pth root of unity to the field of rationals. A prime p is ...

The prime number theorem shows that the nth prime number p_n has the asymptotic value p_n∼nlnn (1) as n->infty (Havil 2003, p. 182). Rosser's theorem makes this a rigorous ...