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  2. Generating set of a group - Wikipedia

    en.wikipedia.org/wiki/Generating_set_of_a_group

    Infinite groups can also have finite generating sets. The additive group of integers has 1 as a generating set. The element 2 is not a generating set, as the odd numbers will be missing. The two-element subset {3, 5} is a generating set, since (−5) + 3 + 3 = 1 (in fact, any pair of coprime numbers is, as a consequence of Bézout's identity).

  3. Salem–Spencer set - Wikipedia

    en.wikipedia.org/wiki/Salem–Spencer_set

    Salem–Spencer sets are also called 3-AP-free sequences or progression-free sets. They have also been called non-averaging sets, [ 1 ] [ 2 ] but this term has also been used to denote a set of integers none of which can be obtained as the average of any subset of the other numbers. [ 3 ]

  4. Generator (mathematics) - Wikipedia

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

    The 5th roots of unity in the complex plane under multiplication form a group of order 5. Each non-identity element by itself is a generator for the whole group. In mathematics and physics, the term generator or generating set may refer to any of a number of related concepts.

  5. Subset - Wikipedia

    en.wikipedia.org/wiki/Subset

    In mathematics, a set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B. The relationship of one set being a subset of another is called inclusion (or sometimes containment).

  6. List of set identities and relations - Wikipedia

    en.wikipedia.org/wiki/List_of_set_identities_and...

    7.2.3.1 Incorrectly distributing by swapping ⋂ and ... The power set of is the set of all subsets of and will be denoted by ℘ = { : }. Universe set and complement ...

  7. Sumset - Wikipedia

    en.wikipedia.org/wiki/Sumset

    In additive combinatorics, the sumset (also called the Minkowski sum) of two subsets and of an abelian group (written additively) is defined to be the set of all sums of an element from with an element from .

  8. 49 Times Crows Were Seen Doing Scarily Smart Things - AOL

    www.aol.com/49-surprising-posts-prove-just...

    Captive New Caledonian Crows Have Even Made Hooked Tools From Wire To Obtain Food Despite Never Having Seen Wire Before Image credits: AGreatWind #41 Crow Engaging In A Phenomenon Called “Anting”.

  9. Complete lattice - Wikipedia

    en.wikipedia.org/wiki/Complete_lattice

    The complete subgroup lattice for D4, the dihedral group of the square. This is an example of a complete lattice. In mathematics, a complete lattice is a partially ordered set in which all subsets have both a supremum and an infimum ().