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A lamp is turned on for 1/2 minute, off for 1/4 minute, on for 1/8 minute, etc. At the end of one minute, the lamp switch will have been moved aleph_0 times, where aleph_0 is ...

A surface of revolution obtained by rotating a closed plane curve about an axis parallel to the plane which does not intersect the curve. The simplest toroid is the torus. ...

The exact values of cos(pi/18) and sin(pi/18) can be given by infinite nested radicals sin(pi/(18))=1/2sqrt(2-sqrt(2+sqrt(2+sqrt(2-...)))), where the sequence of signs +, +, ...

An infinite set, such as the real numbers, which is not countably infinite.

A universal cellular automaton is a cellular automaton which, like a Turing machine, exhibits universality. von Neumann proved that an automaton consisting of cells with four ...

A function f is said to have a upper bound C if f(x)<=C for all x in its domain. The least upper bound is called the supremum. A set is said to be bounded from above if it ...

An optimal filter used for the removal of noise from a signal which is corrupted by the measuring process itself.

Constants gamma such that [int_Omega|f|^qdx]^(1/q)<=gamma[int_Omegasum_(i=1)^N|(partialf)/(partialx_i)|^pdx]^(1/p), where f is a real-valued smooth function on a region Omega ...

A k-matrix is a kind of cube root of the identity matrix (distinct from the identity matrix) which is defined by the complex matrix k=[0 0 -i; i 0 0; 0 1 0]. It satisfies ...

An atlas is a collection of consistent coordinate charts on a manifold, where "consistent" most commonly means that the transition functions of the charts are smooth. As the ...