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Let A be a unital Banach algebra. If a in A and ||1-a||<1, then a^(-1) can be represented by the series sum_(n=0)^(infty)(1-a)^n. This criterion for checking invertibility of ...

An unsolvable problem in logic dating back to the ancient Greeks and quoted, for example, by German philosopher Carl von Prantl (1855). The dilemma consists of a crocodile ...

A solitary number is a number which does not have any friends. Solitary numbers include all primes, prime powers, and numbers for which (n,sigma(n))=1, where (a,b) is the ...

Given three noncollinear points, construct three tangent circles such that one is centered at each point and the circles are pairwise tangent to one another. Then there exist ...

Five or six Wolf prizes are awarded yearly to outstanding living scientists and artists for achievements in the interest of mankind and friendly relations among peoples. In ...

The constant pi, denoted pi, is a real number defined as the ratio of a circle's circumference C to its diameter d=2r, pi = C/d (1) = C/(2r) (2) pi has decimal expansion ...