Proof Theory
Proof theory is a branch of mathematical logic focused on the structure and properties of mathematical proofs. It formalizes reasoning, analyzing how conclusions are derived from axioms and rules.
Proof by Induction
Proof by induction is a powerful mathematical technique used to prove statements for an infinite number of cases. It relies on establishing a base case and then proving an inductive…
Proof by Cases
A method of mathematical proof where a statement is divided into several exhaustive cases. The statement is then proven to be true within each individual case, collectively establishing its validity.
Proof
A logical or mathematical argument that demonstrates the truth of a statement or theorem. Proofs rely on axioms, definitions, and previously established theorems to establish certainty.
Probability Theory
Probability theory is the mathematical study of randomness and uncertainty. It analyzes random variables, events, and processes, providing a framework for understanding and quantifying chance.
Probability Logic
Probability logic extends classical logic to manage uncertainty. It uses probabilistic elements to represent degrees of belief or likelihood, offering a framework for reasoning with incomplete or uncertain information.
Probability Calculus: Understanding Randomness and Events
Probability calculus is the mathematical field dedicated to the study of probability. It provides the laws and formulas essential for analyzing random variables and understanding the likelihood of various events.
Principal Connective in Logic
The principal connective, also known as the dominant connective, is the logical operator that governs the overall structure of a complex proposition in propositional logic. It determines the main division…
Primitive Recursive Relations
A primitive recursive relation is a type of relation definable using primitive recursive functions. These relations represent a subset of computable relations, fundamental in computability theory and logic.
Primitive Recursive Functions Explained
Primitive recursive functions are a subset of computable functions defined using initial functions and operations like composition and primitive recursion. They form a foundational class in computability theory.