Editing Mathematical Logic (section)

== <span style="color: #FFFFFF;">Remembering</span> ==
* '''Mathematical Logic''' — The study of formal systems and the principles of valid reasoning.
* '''Proposition''' — A statement that is either true or false (e.g., "It is raining").
* '''Logical Connectives''' — Symbols used to combine propositions, such as AND ($\land$), OR ($\lor$), NOT ($\neg$), and IF...THEN ($\to$).
* '''Predicate Logic''' — Logic that uses variables and quantifiers (e.g., "For all $x$," "There exists an $x$").
* '''Quantifier''' — Symbols like $\forall$ (For All) and $\exists$ (There Exists).
* '''Axiom''' — A statement that is taken to be true without proof; the starting point of a system.
* '''Theorem''' — A statement that has been proven to be true based on axioms and logic.
* '''Proof''' — A logical argument showing that a statement follows necessarily from axioms.
* '''Consistency''' — A property of a system where no contradictions can be proven (i.e., you can't prove both $A$ and NOT $A$).
* '''Completeness''' — A property where every true statement in the system can be proven.
* '''Decidability''' — A property where there exists an algorithm to determine if any given statement is true or false.
* '''Inference Rule''' — A rule that allows you to derive a new true statement from existing ones (e.g., Modus Ponens).
* '''Symbolic Logic''' — Representing logical arguments using symbols instead of natural language.
* '''Paradox''' — A statement that seems to lead to a contradiction (e.g., "This sentence is false").
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