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The Mertens function is the summary function M(n)=sum_(k=1)^nmu(k), (1) where mu(n) is the Möbius function (Mertens 1897; Havil 2003, p. 208). The first few values are 1, 0, ...

A topology induced by the metric g defined on a metric space X. The open sets are all subsets that can be realized as the unions of open balls B(x_0,r)={x in X|g(x_0,x)<r}, ...

The minimum excluded value. The mex of a set S of nonnegative integers is the least nonnegative integer not in the set.

For a catastrophically unstable recurrence in one direction, any seed values for consecutive x_j and x_(j+1) will converge to the desired sequence of functions in the ...

A function for which all critical points are nondegenerate and all critical levels are different.

A function f(m) is called multiplicative if (m,m^')=1 (i.e., the statement that m and m^' are relatively prime) implies f(mm^')=f(m)f(m^') (Wilf 1994, p. 58). Examples of ...

Given an original knot K, the knots produced by mutations together with K itself are called mutant knots. Mutant knots are often difficult to distinguish. For instance, ...

The "natural exponential function" is the name sometimes given in elementary contexts to the function f(x)=e^x, where e =2.718... is the base of the natural logarithm. While ...

An arrangement of n>=3 points such that n-1 of them are collinear.

The set of nilpotent elements in a commutative ring is an ideal, and it is called the nilradical. Another equivalent description is that it is the intersection of the prime ...