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n events are said to be mutually exclusive if the occurrence of any one of them precludes any of the others. Therefore, for events X_1, ..., X_n, the conditional probability ...

A 10000-sided polygon.

One of the two pieces of a double cone (i.e., two cones placed apex to apex).

mu_i(epsilon), sometimes denoted P_i(epsilon), is the probability that element i is populated, normalized such that sum_(i=1)^Nmu_i(epsilon)=1.

The simplicial complex formed from a family of objects by taking sets that have nonempty intersections.

Approximates the possible values of y in terms of x if sum_(i,j=0)^na_(ij)x^iy^j=0.

An element B of a ring is nilpotent if there exists a positive integer k for which B^k=0.

Given two starting numbers (a_1,a_2), the following table gives the unique sequences {a_i} that contain no three-term arithmetic progressions. Sloane sequence A003278 1, 2, ...

An algebraic surface of degree 9. Enneper's minimal surface is an example of a nonic surface.

A quantity that is nonzero everywhere is said to be nonvanishing. For instance, the values of x^2+1 are nonvanishing for real x, while those of x^2 are not (since x^2 ...