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If a function f(x) is continuous on a closed interval [a,b], then f(x) has both a maximum and a minimum on [a,b]. If f(x) has an extremum on an open interval (a,b), then the ...

An extremum is a maximum or minimum. An extremum may be local (a.k.a. a relative extremum; an extremum in a given region which is not the overall maximum or minimum) or ...

Each of the sacred unit fractions which the ancient Egyptians attributed to the six parts of the eye of the god Horus: 1/2, 1/4, 1/8, 1/16, 1/32, and 1/64. These fractions, ...

A subset F subset R of the real numbers is said to be an F_sigma set provided F is the countable union of closed sets. The name F_sigma comes from French: The F stands for ...

In the course of searching for continued fraction identities, Raayoni (2021) and Elimelech et al. (2023) noticed that while the numerator and denominator of continued ...

A factorion is an integer which is equal to the sum of factorials of its digits. There are exactly four such numbers: 1 = 1! (1) 2 = 2! (2) 145 = 1!+4!+5! (3) 40585 = ...

The determination of a set of factors (divisors) of a given integer ("prime factorization"), polynomial ("polynomial factorization"), etc., which, when multiplied together, ...

In a given acute triangle DeltaABC, find the inscribed triangle whose perimeter is as small as possible. The answer is the orthic triangle of DeltaABC. The problem was ...

A variation of chess involving a change in the form of the board, the rules of play, or the pieces used. For example, the normal rules of chess can be used but with a ...

A functor is said to be faithful if it is injective on maps. This does not necessarily imply injectivity on objects. For example, the forgetful functor from the category of ...