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Homology is a concept that is used in many branches of algebra and topology. Historically, the term "homology" was first used in a topological sense by Poincaré. To him, it ...

Bertrand's postulate, also called the Bertrand-Chebyshev theorem or Chebyshev's theorem, states that if n>3, there is always at least one prime p between n and 2n-2. ...

The general type of homology which is what mathematicians generally mean when they say "homology." Singular homology is a more general version than Poincaré's original ...

For a field K with multiplicative identity 1, consider the numbers 2=1+1, 3=1+1+1, 4=1+1+1+1, etc. Either these numbers are all different, in which case we say that K has ...

Let X be a connected topological space. Then X is unicoherent provided that for any closed connected subsets A and B of X, if X=A union B, then A intersection B is connected. ...

Given a group of n men arranged in a circle under the edict that every mth man will be executed going around the circle until only one remains, find the position L(n,m) in ...

A function has compact support if it is zero outside of a compact set. Alternatively, one can say that a function has compact support if its support is a compact set. For ...

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 ...

Let four lines in a plane represent four roads in general position, and let one traveler T_i be walking along each road at a constant (but not necessarily equal to any other ...

The number 1000000=10^6. While one million in the "American" system of numbers means the same thing as one million in the "British" system, the words billion, trillion, etc., ...