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2. List of set identities and relations - Wikipedia

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

   A universe set is an absorbing element of binary union . The empty set ∅ {\displaystyle \varnothing } is an absorbing element of binary intersection ∩ {\displaystyle \cap } and binary Cartesian product × , {\displaystyle \times ,} and it is also a left absorbing element of set subtraction ∖ : {\displaystyle \,\setminus :}

3. Ring (mathematics) - Wikipedia

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

   A free ring satisfies the universal property: any function from the set X to a ring R factors through F so that F → R is the unique ring homomorphism. Just as in the group case, every ring can be represented as a quotient of a free ring. [46] Now, we can impose relations among symbols in X by taking a quotient.

4. Directed set - Wikipedia

   en.wikipedia.org/wiki/Directed_set

   Here the order relation on the elements of is inherited from ; for this reason, reflexivity and transitivity need not be required explicitly. A directed subset of a poset is not required to be downward closed; a subset of a poset is directed if and only if its downward closure is an ideal. While the definition of a directed set is for an ...

5. Total order - Wikipedia

   en.wikipedia.org/wiki/Total_order

   A binary relation that is antisymmetric, transitive, and reflexive (but not necessarily total) is a partial order. A group with a compatible total order is a totally ordered group. There are only a few nontrivial structures that are (interdefinable as) reducts of a total order. Forgetting the orientation results in a betweenness relation.

6. Boolean algebra - Wikipedia

   en.wikipedia.org/wiki/Boolean_algebra

   In mathematics and mathematical logic, Boolean algebra is a branch of algebra.It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers.

7. Three-valued logic - Wikipedia

   en.wikipedia.org/wiki/Three-valued_logic

   in the redundant binary representation, each digit can have a value of −1, 0, 0/1 (the value 0/1 has two different representations); in the ternary numeral system, each digit is a trit (trinary digit) having a value of: 0, 1, or 2;