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Let A and B be any sets with empty intersection, and let |X| denote the cardinal number of a set X. Then |A|+|B|=|A union B| (Ciesielski 1997, p. 68; Dauben 1990, p. 173; ...

The Euclidean plane parametrized by coordinates, so that each point is located based on its position with respect to two perpendicular lines, called coordinate axes. They are ...

The orthogonal polynomials defined by c_n^((mu))(x) = _2F_0(-n,-x;;-mu^(-1)) (1) = ((-1)^n)/(mu^n)(x-n+1)_n_1F_1(-n;x-n+1;mu), (2) where (x)_n is the Pochhammer symbol ...

The finite simple groups of Lie-type. They include four families of linear simple groups: PSL(n,q) (the projective special linear group), PSU(n,q) (the projective special ...

Clark's triangle is a number triangle created by setting the vertex equal to 0, filling one diagonal with 1s, the other diagonal with multiples of an integer f, and filling ...

Let K be a number field, then each fractional ideal I of K belongs to an equivalence class [I] consisting of all fractional ideals J satisfying I=alphaJ for some nonzero ...

Determining the length of a country's coastline is not as simple as it first appears, as first considered by L. F. Richardson (1881-1953) and sometimes known as the ...

A path in the complex plane over which contour integration is performed to compute a contour integral. When choosing a contour to evaluate an integral on the real line, a ...

Define the correlation integral as C(epsilon)=lim_(N->infty)1/(N^2)sum_(i,j=1; i!=j)^inftyH(epsilon-|x_i-x_j|), (1) where H is the Heaviside step function. When the below ...

A curve of order n is generally determined by n(n+3)/2 points. So a conic section is determined by five points and a cubic curve should require nine. But the Maclaurin-Bézout ...