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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 topological basis is a subset B of a set T in which all other open sets can be written as unions or finite intersections of B. For the real numbers, the set of all open ...

A function f is topologically transitive if, given any two intervals U and V, there is some positive integer k such that f^k(U) intersection V!=emptyset. Vaguely, this means ...

One of a set of numbers defined in terms of an invariant generated by the finite cyclic covering spaces of a knot complement. The torsion numbers for knots up to 9 crossings ...

If one part of the total intersection group of a curve of order n with a curve of order n_1+n_2 constitutes the total intersection with a curve of order n_1, then the other ...

An extension field of a field F that is not algebraic over F, i.e., an extension field that has at least one element that is transcendental over F. For example, the field of ...

The engineering terminology for one use of Fourier transforms. By breaking up a wave pulse into its frequency spectrum f_nu=F(nu)e^(2piinut), (1) the entire signal can be ...

One of Cantor's ordinal numbers omega, omega+1, omega+2, ..., omega+omega, omega+omega+1, ... which is "larger" than any whole number.

Let S(T) be the group of symmetries which map a monohedral tiling T onto itself. The transitivity class of a given tile T is then the collection of all tiles to which T can ...

To translate an object means to perform a translation. A translate of a mathematical object means a shifted (i.e., translated) version of the object. Hence, one can speak of ...