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A module is a mathematical object in which things can be added together commutatively by multiplying coefficients and in which most of the rules of manipulating vectors hold. ...

Let K be a field of arbitrary characteristic. Let v:K->R union {infty} be defined by the following properties: 1. v(x)=infty<=>x=0, 2. v(xy)=v(x)+v(y) forall x,y in K, and 3. ...

The logarithmic integral is defined as the Cauchy principal value li(x) = PVint_0^x(dt)/(lnt) (1) = ...

A vector space V is a set that is closed under finite vector addition and scalar multiplication. The basic example is n-dimensional Euclidean space R^n, where every element ...

There exists a positive integer s such that every sufficiently large integer is the sum of at most s primes. It follows that there exists a positive integer s_0>=s such that ...

A tetradic (or four-way) number is a number that remains unchanged when flipped back to front, mirrored up-down, or flipped up-down. Since the only numbers that remain ...

A fiber bundle (also called simply a bundle) with fiber F is a map f:E->B where E is called the total space of the fiber bundle and B the base space of the fiber bundle. The ...

The series producing Brun's constant converges even if there are an infinite number of twin primes, first proved by Brun (1919).

Grimm conjectured that if n+1, n+2, ..., n+k are all composite numbers, then there are distinct primes p_(i_j) such that p_(i_j)|(n+j) for 1<=j<=k.

The Schnirelmann density of a set of nonnegative integers is the greatest lower bound of the fractions A(n)/n where A(n) is the number of terms in the set <=n.