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Every bounded infinite set in R^n has an accumulation point. For n=1, an infinite subset of a closed bounded set S has an accumulation point in S. For instance, given a ...

If a continuous function defined on an interval is sometimes positive and sometimes negative, it must be 0 at some point. Bolzano (1817) proved the theorem (which effectively ...

The Bombieri p-norm of a polynomial Q(x)=sum_(i=0)^na_ix^i (1) is defined by [Q]_p=[sum_(i=0)^n(n; i)^(1-p)|a_i|^p]^(1/p), (2) where (n; i) is a binomial coefficient. The ...

Let P(E_i) be the probability that E_i is true, and P( union _(i=1)^nE_i) be the probability that at least one of E_1, E_2, ..., E_n is true. Then "the" Bonferroni ...

The Bonne projection is a map projection that resembles the shape of a heart. Let phi_1 be the standard parallel, lambda_0 the central meridian, phi be the latitude, and ...

Every Boolean algebra is isomorphic to the Boolean algebra of sets. The theorem is equivalent to the maximal ideal theorem, which can be proved without using the axiom of ...

Let the values of a function f(x) be tabulated at points x_i equally spaced by h=x_(i+1)-x_i, so f_1=f(x_1), f_2=f(x_2), ..., f_5=f(x_5). Then Boole's rule approximating the ...

A magic square that remains magic when its border is removed. A nested magic square remains magic after the border is successively removed one ring at a time. An example of a ...

There are two types of bordism groups: bordism groups, also called cobordism groups or cobordism rings, and there are singular bordism groups. The bordism groups give a ...

The great success mathematicians had studying hypergeometric functions _pF_q(a_1,...,a_p;b_1,...,b_q;z) for the convergent cases (p<=q+1) prompted attempts to provide ...