Search results
Results from the WOW.Com Content Network
In logic, a set of symbols is commonly used to express logical ... One of this symbol’s uses is to mean “truthmakes” in the truthmaker theory of truth.
1. Naive set theory can mean set theory developed non-rigorously without axioms 2. Naive set theory can mean the inconsistent theory with the axioms of extensionality and comprehension 3. Naive set theory is an introductory book on set theory by Halmos natural The natural sum and natural product of ordinals are the Hessenberg sum and product NCF
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects.Although objects of any kind can be collected into a set, set theory – as a branch of mathematics – is mostly concerned with those that are relevant to mathematics as a whole.
In set theory, each line represents a set instead of a logical statement; A replaces p and B replaces q. When used for sets, a dot above the line represents inclusion, where a dot below represents exclusion. As in logic, basic set operations can be represented visually using R-diagrams:
The theory of finite groups is the set of first-order statements in the language of groups that are true in all finite groups (there are plenty of infinite models of this theory). It is not completely trivial to find any such statement that is not true for all groups: one example is "given two elements of order 2, either they are conjugate or ...
In the case that the index set I is the set of natural numbers, one uses the notation =, which is analogous to that of the infinite sums in series. [11] When the symbol "∪" is placed before other symbols (instead of between them), it is usually rendered as a larger size.
Disjunction: the symbol appeared in Russell in 1908 [6] (compare to Peano's use of the set-theoretic notation of union); the symbol + is also used, in spite of the ambiguity coming from the fact that the + of ordinary elementary algebra is an exclusive or when interpreted logically in a two-element ring; punctually in the history a + together ...
In first-order logic, a predicate forms an atomic formula when applied to an appropriate number of terms. In set theory with the law of excluded middle, predicates are understood to be characteristic functions or set indicator functions (i.e., functions from a set element to a truth value). Set-builder notation makes use of predicates to define ...