Lectures related to Set-theoretic definition of natural numbers

Principle of Double Inclusion

Explains the principle of double inclusion and provides examples with natural numbers and geometry.

Natural Numbers

Covers the concept of natural numbers, including properties like commutativity and associativity.

Recursively Defined Sets and Structures

Explores recursively defined sets, natural numbers, strings, functions, string concatenation, and well-formed formulae.

Function Composition and Integers

Covers function composition and integers, including properties and examples.

Analytic Continuation of Zeta Function

Explores the analytic continuation of the zeta function and its relation to holomorphic functions and natural numbers.

Different Infinities: Cantor's Theorem

Explains Cantor's theorem comparing cardinalities of different number sets.

Place-Valued Arithmetic: Addition and Subtraction

Explores place-valued arithmetic, covering addition, subtraction, and limitations of digital systems.

Counterexample to Induction Theorem

Explores a counterexample to the induction principle, demonstrating a property of natural numbers.

WS1S Solver: Project Structure

Explores the project structure for solving WS1S formulas and planned additions.

Definitions and Examples

Explores the definitions and examples of real number sequences, including arithmetic and geometric sequences.

Least Common Multiple: Basics

Explains the concept of the least common multiple for two natural numbers.

Understanding Equivalence Relations and Integer Construction

Covers the construction of integers through equivalence relations and their properties in mathematics.

Recursively Defined Sets and Structures

Explores recursively defined sets, natural numbers, strings, functions, and propositional logic formulae.

Recurrence: Induction

Covers the principle of induction for natural numbers and the importance of caution in its application.

Sequences and Convergence: Understanding Mathematical Foundations

Covers the concepts of sequences, convergence, and boundedness in mathematics.

Proofs by Induction: Principles and Examples

Explains the induction principle and proofs by induction with examples like 1 + 3 + 5 + ... + (2n-1) = n².

Philosophy of Mathematics: Ontology and Structures

Explores the existence of mathematical objects, truth of propositions, and knowledge about them, covering Platonism, Intuitionism, Structuralism, Nominalism, Logicism, and Formalism.