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Given a hereditary representation of a number n in base b, let B[b](n) be the nonnegative integer which results if we syntactically replace each b by b+1 (i.e., B[b] is a ...

A circle-preserving transformation composed of an odd number of inversions.

The inverse function of the logarithm, defined such that log_b(antilog_bz)=z=antilog_b(log_bz). The antilogarithm in base b of z is therefore b^z.

Consider three mutually tangent circles, and draw their inner Soddy circle. Then draw the inner Soddy circles of this circle with each pair of the original three, and ...

If two quantities A and B are approximately equal, this is written A approx B.

A valuation for which |x|<=1 implies |1+x|<=C for the constant C=1 (independent of x). Such a valuation does not satisfy the strong triangle inequality |x+y|<=max(|x|,|y|).

A group in which any decreasing chain of distinct subgroups terminates after a finite number.

The study of map projections and the making of geographical maps.

The underlying set of the fundamental group of X is the set of based homotopy classes from the circle to X, denoted [S^1,X]. For general spaces X and Y, there is no natural ...

A surface which has no edges.