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A proof of a formula on limits based on the epsilon-delta definition. An example is the following proof that every linear function f(x)=ax+b (a,b in R,a!=0) is continuous at ...

Two matrices A and B are equal to each other, written A=B, if they have the same dimensions m×n and the same elements a_(ij)=b_(ij) for i=1, ..., n and j=1, ..., m. ...

The series sumf(n) for a monotonic nonincreasing f(x) is convergent if lim_(x->infty)^_(e^xf(e^x))/(f(x))<1 and divergent if lim_(x->infty)__(e^xf(e^x))/(f(x))>1.

A more common way to describe a Euclidean ring.

A weighted graph in which the weights are equal to the Euclidean lengths of the edges in a specified embedding (Skiena 1990, pp. 201 and 252).

The derivative (deltaL)/(deltaq)=(partialL)/(partialq)-d/(dt)((partialL)/(partialq^.)) appearing in the Euler-Lagrange differential equation.

Consider a function f(x) in one dimension. If f(x) has a relative extremum at x_0, then either f^'(x_0)=0 or f is not differentiable at x_0. Either the first or second ...

A line segment connecting nonadjacent polyhedron vertices sharing a common face in a parallelepiped or other similar solid.

Using a set of corners of a solid that lie in a plane to form the polygon vertices of a new polygon is called faceting. Such polygons may outline new faces that join to ...

A statement which is rigorously not true. Regular two-valued logic allows statements to be only true or false, but fuzzy logic treats "truth" as a continuum which can have a ...