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Monster-barring is a term coined by Lakatos (1976) to refer to the refining of a hypothesis to rule out nasty counterexamples (Bailey et al. 2007, p. 11).

The hypothesis is that, for X is a measure space, f_n(x)->f(x) for each x in X, as n->infty. The hypothesis may be weakened to almost everywhere convergence.

Let m and m+h be two consecutive critical indices of f and let F be (m+h)-normal. If the polynomials p^~_k^((n)) are defined by p^~_0^((n))(u) = 1 (1) p^~_(k+1)^((n))(u) = ...

The line R[s]=1/2 in the complex plane on which the Riemann hypothesis asserts that all nontrivial (complex) Riemann zeta function zeros lie. The plot above shows the first ...

Li's criterion states that the Riemann hypothesis is equivalent to the statement that, for lambda_n=1/((n-1)!)(d^n)/(ds^n)[s^(n-1)lnxi(s)]|_(s=1), (1) where xi(s) is the ...

A test used to determine the statistical significance of an observation. Two main types of error can occur: 1. A type I error occurs when a false negative result is obtained ...

Consider the inequality sigma(n)<e^gammanlnlnn for integer n>1, where sigma(n) is the divisor function and gamma is the Euler-Mascheroni constant. This holds for 7, 11, 13, ...

Voronin (1975) proved the remarkable analytical property of the Riemann zeta function zeta(s) that, roughly speaking, any nonvanishing analytic function can be approximated ...

An alpha value is a number 0<=alpha<=1 such that P(z>=z_(observed))<=alpha is considered "significant," where P is a P-value.

The probability that a variate would assume a value greater than or equal to the observed value strictly by chance: P(z>=z_(observed)).