A Number Sense as an Emergent Property of the Manipulation Brain
Explore how number sense emerges from brain manipulation, examining experiments, perceptions, and the role of supervised learning in developing numerical understanding.
Real Numbers
Comprehensive overview of real numbers, covering rational and irrational numbers, integers, and decimals. Includes practice problems and examples for better understanding.
A Multiset Approach to Arithmetic - Math Foundations
Explore a new framework for arithmetic using multisets, introducing natural numbers, polynumbers, and multinumbers. Learn innovative definitions and operations that offer profound insights into mathematical structures.
How to Set Up Fractions IV - The Relation Between Fractions and Other Number Systems
Explore number systems, focusing on rational numbers and their relationships. Challenges traditional views on real numbers, emphasizing the distinction between counting and measuring in mathematics.
The Realm of Natural Numbers - Data Structures in Mathematics
Explore natural numbers through multisets, examining addition, union, and intersection operations. Discover unique properties, including a new distributive law that forms the basis for tropical calculus.
Absolute Versus Relative Measurements in Geometry - Rational Geometry Math Foundations
Explore the distinction between absolute and relative measurements in geometry, focusing on proportions and ratios. Learn about ancient Greek approaches and their relevance to modern mathematics.
Divisibility of Big Numbers - Data Structures in Mathematics Math Foundations
Explore divisibility of large numbers, modular arithmetic, and long division techniques. Learn key concepts and practical applications in number theory and mathematical foundations.
Arithmetical Expressions as Natural Numbers - Data Structures in Mathematics Math Foundations
Explores the complexities of representing large numbers through arithmetical expressions, discussing limitations, logical issues, and the challenges of creating a coherent system for such representations.
The Hindu Arabic Number System Revisited - Data Structures in Mathematics Math Foundations
Explores three approaches to Hindu Arabic numerals, examining their mathematical foundations and practical applications in arithmetic and number representation.
Naming and Ordering Numbers for Students - Data Structures in Mathematics Math Foundations
Explores naming, ordering, and using natural numbers, focusing on their fundamental nature as expressions of marks. Discusses counting, cardinal vs ordinal usage, and the successor operation.
The Essential Dichotomy Underlying Mathematics - Data Structures Math Foundations
Explore the fundamental dichotomy underlying mathematics, challenging traditional views on natural numbers and geometry to uncover the core essence of mathematical thinking.
The Sporadic Nature of Big Numbers - Data Structures in Mathematics
Explores how arithmetic breaks down with large numbers, revealing most "numbers" are invisible to us. Challenges conventional number theory and questions the nature of natural numbers.
The Chaotic Complexity of Natural Numbers - Data Structures in Mathematics
Exploring the complex nature of arithmetic with large numbers, focusing on exponential and triangular complexity, and examining the role of powers in mathematical computations.
Maxel Algebra I - Data Structures in Mathematics Math Foundations
Explore maxel algebra, a new matrix theory focusing on idempotent diagonal maxels and sets of natural numbers. Learn about multiplication, identity maxels, and key propositions in this mathematical foundation.
Measurement, Approximation and Interval Arithmetic - Real Numbers and Limits Math Foundations
Explore interval arithmetic, its laws for natural numbers and integers, and the challenges with real number arithmetic. Gain insights into measurement, approximation, and foundational mathematical concepts.
Measurement, Approximation and Interval Arithmetic - Real Numbers and Limits Math Foundations
Explores interval arithmetic for natural numbers and integers, covering definitions, inequalities, arithmetic operations, and applications in measurement and counting. Lays foundations for mathematical reasoning.
The Division Algorithm for Polynumbers - Arithmetic + Geometry Math Foundations | N J Wildberger
Explore the division algorithm for polynumbers, covering integral and rational polynumbers, and different approaches to division. Learn foundational concepts in mathematics with a focus on logical rigor.
Infinity in Greek Mathematics - Math History - NJ Wildberger
Explore ancient Greek mathematics, focusing on Eudoxus and Archimedes' groundbreaking work in calculus, geometry, and mechanics. Discover their ingenious formulas and principles that laid the foundation for modern mathematics.
The Division Algorithm - Number Theory
Explore the division algorithm in number theory, covering natural numbers, division with remainder, and related concepts through clear explanations and exercises.
TREE vs Graham's Number - Numberphile
Explore the mind-bending concept of TREE vs Graham's Number, delving into successor functions, ordinal infinity, and the vastness of mathematical concepts beyond comprehension.
Reconsidering Natural Numbers and Arithmetical Expressions - Math Foundations 185
Exploring the foundations of arithmetic, redefining natural numbers, and challenging traditional notions of prime numbers and infinity in mathematics.