mathematical

The Indispensability Argument in Philosophy of Mathematics

This argument posits that if mathematical entities are essential for our most successful scientific theories, we should accept their existence.…

3 weeks ago

The Identity Function: Understanding Input and Output

The identity function is a fundamental concept in mathematics and computer science. It's a function that takes an input and…

3 weeks ago

Henkin Sentence

A Henkin sentence is a self-referential statement that asserts its own provability within a formal system. It's a foundational concept…

3 weeks ago

Gödel’s Second Incompleteness Theorem

Gödel's second incompleteness theorem states that no consistent formal system strong enough to include basic arithmetic can prove its own…

3 weeks ago

Gödel’s First Incompleteness Theorem

Gödel's First Incompleteness Theorem states that any consistent formal system capable of basic arithmetic contains true statements that are unprovable…

3 weeks ago

Gödel Numbering

Gödel numbering assigns unique natural numbers to symbols, formulas, and proofs in formal systems. This allows mathematical statements to be…

3 weeks ago

Glivenko’s Theorem

Glivenko's theorem in logic connects classical and intuitionistic systems. It states that any formula provable in classical logic is also…

3 weeks ago

Understanding Mathematical Functions

A function is a fundamental mathematical concept establishing a precise relationship between sets. It ensures each input from the first…

3 weeks ago

Fixed Point: Understanding Mathematical and Logical Stability

A fixed point is a value that remains unchanged when a specific function or operation is applied to it. This…

3 weeks ago

Finite Model Theory

Finite model theory explores structures with finite domains. It investigates properties and expressiveness of logical languages within these finite settings,…

3 weeks ago