set theory

Relative Consistency Proof

A relative consistency proof demonstrates that if a system S is consistent, adding new axioms to S also maintains consistency.…

4 days ago

Reflexivity in Relations

Reflexivity means every element in a set is related to itself. This fundamental property is crucial in understanding various mathematical…

4 days ago

Ramified Theory of Types

An extension of the simple theory of types, the ramified theory introduces levels to distinguish objects and functions by order,…

4 days ago

Quantifiers in Logic

Quantifiers are fundamental logical operators like 'all' or 'some' that specify the quantity of elements in a domain satisfying a…

4 days ago

Propositional Function Explained

A propositional function is an expression with variables that becomes a true or false proposition when those variables are assigned…

4 days ago

Pairing Function

A pairing function maps pairs of natural numbers to a single natural number, preserving uniqueness. This allows ordered pairs to…

4 days ago

Ordered Pair

An ordered pair is a fundamental mathematical structure containing two elements in a specific sequence, denoted as (a, b). Order…

4 days ago

Onto: Understanding Surjective Functions

An onto function, also known as a surjective function, maps elements from one set to another, ensuring every element in…

4 days ago

One-to-One Function (Injective)

A one-to-one function maps each element from its domain to a unique element in its codomain. This ensures no two…

4 days ago

Objectual Quantifiers in Formal Logic

Objectual quantifiers are a type of quantifier in formal logic that specifically refer to objects within the domain of discourse,…

4 days ago