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A quantity which remains unchanged under certain classes of transformations. Invariants are extremely useful for classifying mathematical objects because they usually reflect ...

A map is a way of associating unique objects to every element in a given set. So a map f:A|->B from A to B is a function f such that for every a in A, there is a unique ...

A proof which indirectly shows a mathematical object exists without providing a specific example or algorithm for producing an example. Nonconstructive proofs are also called ...

A group or other algebraic object is called non-Abelian if the law of commutativity does not always hold, i.e., if the object is not Abelian. For example, the group of ...

A class of illusion in which an object which is physically unrealizable is apparently depicted. More than 100 papers have been written about impossible figures (Kulpa 1987), ...

The word basis can arise in several different contexts. Speaking in general terms, an object is "generated" by a basis in whatever manner is appropriate. For example, a ...

A mathematical structure A is said to be closed under an operation + if, whenever a and b are both elements of A, then so is a+b. A mathematical object taken together with ...

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 puzzle in which one object is to be converted to another by making a finite number of cuts and reassembling it. The cuts are often, but not always, restricted to straight ...

The infinitesimal algebraic object associated with a Lie groupoid. A Lie algebroid over a manifold B is a vector bundle A over B with a Lie algebra structure [,] (Lie ...