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Consecutive number sequences are sequences constructed by concatenating numbers of a given type. Many of these sequences were considered by Smarandache and so are sometimes ...

If the consistency of one of two propositions implies the consistency of the other, the first is said to have greater consistency strength.

A topological space.

No A is not-A.

An immediate consequence of a result already proved. Corollaries usually state more complicated theorems in a language simpler to use and apply.

x^(2n)+1=[x^2-2xcos(pi/(2n))+1] ×[x^2-2xcos((3pi)/(2n))+1]×...× ×[x^2-2xcos(((2n-1)pi)/(2n))+1].

The largest n such that |z_n|<4 in a Mandelbrot set. Points of different count are often assigned different colors.

If r experiments are performed with n_i possible outcomes for each experiment i=1,2,...,r, then there are a total of product_(i=1)^(r)n_i possible outcomes.

If X and Y are independent variates and X+Y is a normal distribution, then both X and Y must have normal distributions. This was proved by Cramér in 1936.

Exchanges branches of the hyperbola x^'y^'=xy. x^' = mu^(-1)x (1) y^' = -muy. (2)