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  2. Subset - Wikipedia

    en.wikipedia.org/wiki/Subset

    A is a subset of B (denoted ) and, conversely, B is a superset of A (denoted ). 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.

  3. Glossary of set theory - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_set_theory

    2. A proper subset of a set X is a subset not equal to X. 3. A proper forcing is a forcing notion that does not collapse any stationary set 4. The proper forcing axiom asserts that if P is proper and D α is a dense subset of P for each α<ω 1, then there is a filter G P such that D α ∩ G is nonempty for all α<ω 1

  4. Dedekind-infinite set - Wikipedia

    en.wikipedia.org/wiki/Dedekind-infinite_set

    In mathematics, a set A is Dedekind-infinite (named after the German mathematician Richard Dedekind) if some proper subset B of A is equinumerous to A. Explicitly, this means that there exists a bijective function from A onto some proper subset B of A. A set is Dedekind-finite if it is not Dedekind-infinite (i.e., no such bijection exists).

  5. Subclass (set theory) - Wikipedia

    en.wikipedia.org/wiki/Subclass_(set_theory)

    In fact, when using a definition of classes that requires them to be first-order definable, it is enough that B be a set; the axiom of specification essentially says that A must then also be a set. As with subsets, the empty set is a subclass of every class, and any class is a subclass of itself. But additionally, every class is a subclass of ...

  6. Subgroup - Wikipedia

    en.wikipedia.org/wiki/Subgroup

    A proper subgroup of a group G is a subgroup H which is a proper subset of G (that is, H ≠ G). This is often represented notationally by H < G, read as "H is a proper subgroup of G". Some authors also exclude the trivial group from being proper (that is, H ≠ {e} ). [2] [3] If H is a subgroup of G, then G is sometimes called an overgroup of H.

  7. Sum-free set - Wikipedia

    en.wikipedia.org/wiki/Sum-free_set

    In additive combinatorics and number theory, a subset A of an abelian group G is said to be sum-free if the sumset A + A is disjoint from A. In other words, A is sum-free if the equation a + b = c {\displaystyle a+b=c} has no solution with a , b , c ∈ A {\displaystyle a,b,c\in A} .

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