Subtraction is a fundamental arithmetic operation. It involves finding the difference between two numbers, known as the minuend and the…
Cardinal numerals represent quantity, answering 'how many?'. They are fundamental to counting, measurement, and basic arithmetic, forming the bedrock of…
The successor function, denoted S(n) = n + 1, is a foundational concept in arithmetic and logic, defining the next…
A non-standard model adheres to a theory's axioms but possesses unintended properties. It's crucial for demonstrating a theory's consistency and…
Neo-Fregeanism revives Frege's logicist project, aiming to base mathematics on logic. It utilizes Hume's Principle and other axioms to ground…
The set of positive integers, often denoted by N, typically including zero. Natural numbers form the foundation for counting, ordering,…
Gödel's First Incompleteness Theorem states that any consistent formal system capable of basic arithmetic contains true statements that are unprovable…
Frege's theorem establishes that arithmetic is reducible to logic. It demonstrates how basic arithmetic principles can be derived from logical…
Commutativity is a fundamental property in mathematics where the order of operands in a binary operation does not affect the…