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An object is said to be self-similar if it looks "roughly" the same on any scale. Fractals are a particularly interesting class of self-similar objects. Self-similar objects ...

The weak law of large numbers (cf. the strong law of large numbers) is a result in probability theory also known as Bernoulli's theorem. Let X_1, ..., X_n be a sequence of ...

The sequence of variates X_i with corresponding means mu_i obeys the strong law of large numbers if, to every pair epsilon,delta>0, there corresponds an N such that there is ...

The group of an elliptic curve which has been transformed to the form y^2=x^3+ax+b is the set of K-rational points, including the single point at infinity. The group law ...

A scale-free network is a connected graph or network with the property that the number of links k originating from a given node exhibits a power law distribution ...

No A is not-A.

If bc=bd (mod a) and (b,a)=1 (i.e., a and b are relatively prime), then c=d (mod a).

cos(20 degrees)cos(40 degrees)cos(80 degrees)=1/8. An identity communicated to Feynman as a child by a boy named Morrie Jacobs (Gleick 1992, p. 47). Feynman remembered this ...

The theorem in set theory and logic that for all sets A and B, B=(A intersection B^_) union (B intersection A^_)<=>A=emptyset, (1) where A^_ denotes complement set of A and ...

A metatheorem stating that every theorem on partially ordered sets remains true if all inequalities are reversed. In this operation, supremum must be replaced by infimum, ...