Concepts related to logic and computational theory

Collections: See sets and function-related definitions
Mappings: See sets and function-related definitions
Full shot: See Set and Function-related definitions
Single shot: See Set and Function-related definitions
Relationships: See sets and function-related definitions
Reflexive relationships: See sets and function-related definitions
Transitive relationships: See Collections and Function-related definitions
Symmetric relationships: See sets and function-related definitions
Equivalence relationship: A relationship satisfies reflexive, transitive, or symmetric, it is called an equivalence relation
Natural number Set N: What we usually see by 0,1,2,3,4 ... A collection of components
Real set R: Usually the number we can see is this.
Complex set C: The set of roots of algebraic equations
Algebraic number: A number is an algebraic number, and only if it is the root of a polynomial equation of integral coefficients
Transcendental Number: The number of other numbers in the set that are removed from the algebraic number is the transcendental number, such as E, PI, etc.
Equipotential: Between two sets, if there is a double shot, they are said to be equal, such as [0,1] and [3,4], denoted by a symbol ~. Obviously, the equipotential is an equivalence relationship.
P-Set: The set of problems that can be received by deterministic Turing is called P-sets
NP set: A set of problems that can be received by a non-deterministic Turing group called NP sets
Computable: Do not understand the concept, do not see
First order logic: a reasoning system consisting of arbitrary quantifier symbols, negative logic symbols, combined logical symbols, propositional symbols, Chang-won symbols (plainly, first-order logic does not allow characterization of variables)
Syntax tree: An inference tree, the syntax tree, that is inferred using axioms and inference rules
Proof tree: If the leaf node of a grammar tree is a proposition that is not in the axiom set, the syntax tree is said to be the proof tree of this proposition.
Logic true (abbreviation is true): a given proposition, the corresponding system of arbitrary interpretation and assignment, the proposition is true, then called the proposition is true, that is, logic is true.
Proof (that is, what we often say): There is a proof tree in a proposition, it is said that the proposition is provable
Completeness: The logic of the true proposition must be able to prove that the system is complete
Correctness: What can be proved is logically true, it is said that the system is correct
Godel theorem of incompleteness: Any system containing arithmetic logic has a proposition that is logically true but not provable
Arieful 0: A set and a set of natural numbers and other potentials, it is said that the potential of the set is arieful 0
Arieful: The potential of a set and a real number is said to be arieful
Continuum hypothesis: There is no other potential between arieful and arieful 0.

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Concepts related to logic and computational theory