The image of a function represents the set of all possible output values derived from its input domain. It's a…
Hume's principle states that two collections have the same number of objects if and only if a one-to-one correspondence can…
A hierarchy ranks entities based on criteria, seen in organizational structures and set theory. Tarski's and cumulative hierarchies are key…
A hereditary property in mathematics and logic is a characteristic that, if held by an object, is also present in…
The field of a function encompasses both its domain (inputs) and its range (outputs). It represents the complete set of…
Extensional logic focuses on the actual sets of things terms refer to, rather than their meanings. Truth depends only on…
Extension refers to the set of all things a term or concept applies to, contrasting with its intension, which defines…
A Euclidean relation is a property of a binary relation R. If an element x is related to both y…
An equivalence relation is a fundamental concept in mathematics. It's a binary relation that is reflexive, symmetric, and transitive, establishing…
The downward Löwenheim–Skolem theorem states that if a theory has an infinite model, it has a model of every infinite…