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- Propositional_function abstract "A propositional function in logic, is a sentence expressed in a way that would assume the value of true or false, except that within the sentence is a variable (x) that is not defined or specified, which leaves the statement undetermined. Of course, the sentence can consist of several such variables (e.g. n variables, in which case the function takes n arguments).As a mathematical function, A(x) or A(x1, x2, · · ·, xn), the propositional function is abstracted from predicates or propositional forms. As an example, let's imagine the predicate, \"x is hot\". The substitution of any entity for x will produce a specific proposition that can be described as either true or false, even though \"x is hot\" on its own has no value as either a true or false statement. However, when you assign x a value, such as lava, the function then has the value true; while if you assign x a value like ice, the function then has the value false.Propositional functions are useful in set theory for the formation of sets. For example, in 1903 Bertrand Russell wrote in The Principles of Mathematics (page 106):\"...it has become necessary to take propositional function as a primitive notion.Later Russell examined the problem of whether propositional functions were predicative or not, and he proposed two theories to try to get at this question: the zig-zag theory and the ramified theory of types.A Propositional Function, or a predicate, in a variable x is a sentence p(x) involving x that becomes a proposition when we give x a definite value from the set of values it can take.".
- Propositional_function wikiPageID "229146".
- Propositional_function wikiPageLength "2700".
- Propositional_function wikiPageOutDegree "22".
- Propositional_function wikiPageRevisionID "694192899".
- Propositional_function wikiPageWikiLink Bertrand_Russell.
- Propositional_function wikiPageWikiLink Boolean-valued_function.
- Propositional_function wikiPageWikiLink Category:Concepts_in_logic.
- Propositional_function wikiPageWikiLink Category:Functions_and_mappings.
- Propositional_function wikiPageWikiLink Category:Logical_expressions.
- Propositional_function wikiPageWikiLink Category:Mathematical_relations.
- Propositional_function wikiPageWikiLink Category:Predicate_logic.
- Propositional_function wikiPageWikiLink Contradiction.
- Propositional_function wikiPageWikiLink Function_(mathematics).
- Propositional_function wikiPageWikiLink Ice.
- Propositional_function wikiPageWikiLink Lava.
- Propositional_function wikiPageWikiLink Logic.
- Propositional_function wikiPageWikiLink Predicate_(mathematical_logic).
- Propositional_function wikiPageWikiLink Primitive_notion.
- Propositional_function wikiPageWikiLink Sentence_(logic).
- Propositional_function wikiPageWikiLink Set_(mathematics).
- Propositional_function wikiPageWikiLink Set_theory.
- Propositional_function wikiPageWikiLink The_Principles_of_Mathematics.
- Propositional_function wikiPageWikiLink Truth.
- Propositional_function wikiPageWikiLink Variable_(mathematics).
- Propositional_function wikiPageWikiLink Well-formed_formula.
- Propositional_function wikiPageWikiLinkText "Propositional function".
- Propositional_function wikiPageWikiLinkText "predicates".
- Propositional_function wikiPageWikiLinkText "propositional function".
- Propositional_function wikiPageUsesTemplate Template:Mergefrom.
- Propositional_function wikiPageUsesTemplate Template:Reflist.
- Propositional_function wikiPageUsesTemplate Template:Sub.
- Propositional_function subject Category:Concepts_in_logic.
- Propositional_function subject Category:Functions_and_mappings.
- Propositional_function subject Category:Logical_expressions.
- Propositional_function subject Category:Mathematical_relations.
- Propositional_function subject Category:Predicate_logic.
- Propositional_function hypernym Sentence.
- Propositional_function type Person.
- Propositional_function type Concept.
- Propositional_function type Function.
- Propositional_function type Relation.
- Propositional_function comment "A propositional function in logic, is a sentence expressed in a way that would assume the value of true or false, except that within the sentence is a variable (x) that is not defined or specified, which leaves the statement undetermined. Of course, the sentence can consist of several such variables (e.g.".
- Propositional_function label "Propositional function".
- Propositional_function sameAs Q3606768.
- Propositional_function sameAs Función_proposicional.
- Propositional_function sameAs گزارهنما.
- Propositional_function sameAs 命題関数.
- Propositional_function sameAs m.019bpb.
- Propositional_function sameAs Q3606768.
- Propositional_function wasDerivedFrom Propositional_function?oldid=694192899.
- Propositional_function isPrimaryTopicOf Propositional_function.