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The paradox of a man who states "I am lying." If he is lying, then he is telling the truth, and vice versa. Another version of this paradox is the Epimenides paradox. Such ...

The Wythoff array is an interspersion array that can be constructed by beginning with the Fibonacci numbers {F_2,F_3,F_4,F_5,...} in the first row and then building up ...

Propositional calculus is the formal basis of logic dealing with the notion and usage of words such as "NOT," "OR," "AND," and "implies." Many systems of propositional ...

The property of being continuous.

A definition assigns properties to some sort of mathematical object. For example, Euclid's Elements starts with a number of definitions, such as "a line is a breadthless ...

A property that passes from a topological space to all its quotient spaces. This is true for connectedness, local connectedness and separability, but not for any of the ...

A function between categories which maps objects to objects and morphisms to morphisms. Functors exist in both covariant and contravariant types.

A branch of mathematics which attempts to formalize the nature of the set using a minimal collection of independent axioms. Unfortunately, as discovered by its earliest ...

Nonstandard analysis is a branch of mathematical logic which introduces hyperreal numbers to allow for the existence of "genuine infinitesimals," which are numbers that are ...

The number of "arrangements" in an ordering of n items is given by either a combination (order is ignored) or a permutation (order is significant). An ordering (or order) is ...