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The determination of the number of monotone Boolean functions of n variables (equivalent to the number of antichains on the n-set {1,2,...,n}) is called Dedekind's problem, ...

Elementary methods consist of arithmetic, geometry, and high school algebra. These are the only tools that may be used in the branch of number theory known as elementary ...

The least number of crossings that occur in any projection of a link. In general, it is difficult to find the crossing number of a given link. Knots and links are generally ...

A multiple of a number x is any quantity y=nx with n an integer. If x and y are integers, then x is called a factor of y. The smallest positive number m for which there exist ...

A quantity which does not equal zero is said to be nonzero. A real nonzero number must be either positive or negative, and a complex nonzero number can have either real or ...

The length of a number n in base b is the number of digits in the base-b numeral for n, given by the formula L(n,b)=|_log_b(n)_|+1, where |_x_| is the floor function. The ...

The ratio of two numbers r and s is written r/s, where r is the numerator and s is the denominator. The ratio of r to s is equivalent to the quotient r/s. Betting odds ...

To color any map on the sphere or the plane requires at most six-colors. This number can easily be reduced to five, and the four-color theorem demonstrates that the necessary ...

For any ordinal number alpha, the successor of alpha is alpha union {alpha} (Ciesielski 1997, p. 46). The successor of an ordinal number alpha is therefore the next ordinal, ...

Let G be a graph and S a subgraph of G. Let the number of odd components in G-S be denoted S^', and |S| the number of graph vertices of S. The condition |S|>=S^' for every ...