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The set of all sets is its own power set. Therefore, the cardinal number of the set of all sets must be bigger than itself.

The function from a given nonempty set X to the power set P(X) that maps every element x of X to the set {x}.

The set of points, known as boundary points, which are members of the set closure of a given set S and the set closure of its complement set. The boundary is sometimes called ...

A sum is the result of an addition. For example, adding 1, 2, 3, and 4 gives the sum 10, written 1+2+3+4=10. (1) The numbers being summed are called addends, or sometimes ...

A superset which is not the entire set.

Let a knot K be parameterized by a vector function v(t) with t in S^1, and let w be a fixed unit vector in R^3. Count the number of local minima of the projection function ...

In 1803, Malfatti posed the problem of determining the three circular columns of marble of possibly different sizes which, when carved out of a right triangular prism, would ...

If at least one solution can be determined for a given problem, a solution to that problem is said to exist. Frequently, mathematicians seek to prove the existence of ...

The term "God's number" is sometimes given to the graph diameter of Rubik's graph, which is the minimum number of turns required to solve a Rubik's cube from an arbitrary ...

Given n circles and a perimeter p, the total area of the convex hull is A_(Convex Hull)=2sqrt(3)(n-1)+p(1-1/2sqrt(3))+pi(sqrt(3)-1). Furthermore, the actual area equals this ...