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An infinitesimal is some quantity that is explicitly nonzero and yet smaller in absolute value than any real quantity. The understanding of infinitesimals was a major ...

Let G be a group, then there exists a piecewise linear knot K^(n-2) in S^n for n>=5 with G=pi_1(S^n-K) iff G satisfies 1. G is finitely presentable, 2. The Abelianization of ...

The numbers B_(n,k)(1!,2!,3!,...)=(n-1; k-1)(n!)/(k!), where B_(n,k) is a Bell polynomial.

A graph for which every node has finite degree.

A branch point whose neighborhood of values wrap around an infinite number of times as their complex arguments are varied. The point z=0 under the function lnz is therefore a ...

In abstract topology, a machine is method for producing infinite loop spaces and spectra. In automata theory, an abstract machine that is implemented in hardware is simply ...

An infinite-dimensional differential calculus on the Wiener space, also called stochastic calculus of variations.

For an infinite population with mean mu, variance sigma^2, skewness gamma_1, and kurtosis excess gamma_2, the corresponding quantities for the distribution of means are ...

(e^(ypsi_0(x))Gamma(x))/(Gamma(x+y))=product_(n=0)^infty(1+y/(n+x))e^(-y/(n+x)), where psi_0(x) is the digamma function and Gamma(x) is the gamma function.

Let (A,<=) and (B,<=) be well ordered sets with ordinal numbers alpha and beta. Then alpha<beta iff A is order isomorphic to an initial segment of B (Dauben 1990, p. 199). ...