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2. Ménage problem - Wikipedia

   en.wikipedia.org/wiki/Ménage_problem

   In a reduced diagram, the two labels at a crossing cannot be consecutive, so the set of pairs of labels at each crossing, used in Dowker notation to represent the knot, can be interpreted as a perfect matching in a graph that has a vertex for every number in the range from 1 to 2n and an edge between every pair of numbers that has different ...

3. Four fours - Wikipedia

   en.wikipedia.org/wiki/Four_fours

   For example, when d=4, the hash table for two occurrences of d would contain the key-value pair 8 and 4+4, and the one for three occurrences, the key-value pair 2 and (4+4)/4 (strings shown in bold). The task is then reduced to recursively computing these hash tables for increasing n , starting from n=1 and continuing up to e.g. n=4.

4. Equinumerosity - Wikipedia

   en.wikipedia.org/wiki/Equinumerosity

   Assuming the existence of an infinite set N consisting of all natural numbers and assuming the existence of the power set of any given set allows the definition of a sequence N, P(N), P(P(N)), P(P(P(N))), … of infinite sets where each set is the power set of the set preceding it. By Cantor's theorem, the cardinality of each set in this ...

5. Equality (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Equality_(mathematics)

   In set theory, any two sets are defined to be equal if they have all the same members. This is called the Axiom of extensionality . Usually set theory is defined within logic, and therefore uses the equality described above, however, if a logic system does not have equality, it is possible to define equality within set theory.

6. Bijective proof - Wikipedia

   en.wikipedia.org/wiki/Bijective_proof

   In combinatorics, bijective proof is a proof technique for proving that two sets have equally many elements, or that the sets in two combinatorial classes have equal size, by finding a bijective function that maps one set one-to-one onto the other. This technique can be useful as a way of finding a formula for the number of elements of certain ...

7. Set (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Set_(mathematics)

   A set of polygons in an Euler diagram This set equals the one depicted above since both have the very same elements.. In mathematics, a set is a collection of different [1] things; [2] [3] [4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other ...