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A limiting case in which a class of object changes its nature so as to belong to another, usually simpler, class. For example, the point is a degenerate case of the circle as ...

The set containing no elements, commonly denoted emptyset or emptyset, the former of which is used in this work. These correspond to Wolfram Language and TeX characters ...

An object is unique if there is no other object satisfying its defining properties. An object is said to be essentially unique if uniqueness is only referred to the ...

The Hodge conjecture asserts that, for particularly nice types of spaces called projective algebraic varieties, the pieces called Hodge cycles are actually rational linear ...

A real-valued univariate function f=f(x) has a jump discontinuity at a point x_0 in its domain provided that lim_(x->x_0-)f(x)=L_1<infty (1) and lim_(x->x_0+)f(x)=L_2<infty ...

The term "loop" has a number of meanings in mathematics. Most simply, a loop is a closed curve whose initial and final points coincide in a fixed point p known as the ...

In a set X equipped with a binary operation · called a product, the multiplicative identity is an element e such that e·x=x·e=x for all x in X. It can be, for example, the ...

de Rham cohomology is a formal set-up for the analytic problem: If you have a differential k-form omega on a manifold M, is it the exterior derivative of another differential ...

A finite group G has a finite number of conjugacy classes and a finite number of distinct irreducible representations. The group character of a group representation is ...

The game of tic-tac-toe, also spelled ticktacktoe and also known as 3-in-a-row or "naughts and crosses," is a game in which players alternate placing pieces (typically Xs for ...