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#Rational Numbers

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Real Numbers CBSE Class 10

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Comprehensive exploration of real numbers for 10th grade, covering number systems, Euclid's lemma, HCF, fundamental theorem of arithmetic, and irrational numbers.
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9 Lesons
1 hour 30 minutes
On-Demand
Free-Video

Algebra 1 Course - Unit 10

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Comprehensive exploration of rational numbers, square roots, radicals, and the Pythagorean theorem, with practical applications in solving equations and understanding fractional exponents.
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33 Lesons
2 hours 30 minutes
On-Demand
Free-Video

Grade 9 Mathematics Unit 1 Relation

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Comprehensive exploration of number systems, operations, and mathematical concepts for Ethiopian Grade 9 students, covering rational, irrational, and real numbers, radicals, and more.
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10 Lesons
5 hours
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

A Importância da Esquecida Representação Decimal de Números Racionais - PAPMEM Janeiro 2023

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Explore a representação decimal de números racionais, aprimorando o ensino de matemática no Ensino Médio. Aprenda técnicas para melhorar a compreensão dos alunos sobre este tópico fundamental.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

On the Dani Correspondence and Its Applications - Lecture 3

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Delve into ergodic theory and dynamics applications in Diophantine approximation, exploring Dani's correspondence and its impact on understanding rational number density patterns.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
The Organic Chemistry Tutor

Real Numbers

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Comprehensive overview of real numbers, covering rational and irrational numbers, integers, and decimals. Includes practice problems and examples for better understanding.
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5 Lesons
25 minutes
On-Demand
Free-Video
Insights into Mathematics

Numbers and Arithmetic - Math Terminology

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A comprehensive review of fundamental mathematical concepts and terminology for university-level math, covering number systems, arithmetic operations, fractions, and basic number theory.
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8 Lesons
25 minutes
On-Demand
Free-Video
Insights into Mathematics

Algebraic Number Theory and Rings I - Math History - NJ Wildberger

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Explore algebraic number theory and rings, focusing on extension fields, Gaussian integers, and the development of abstract ring theory in 19th-century mathematics.
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7 Lesons
48 minutes
On-Demand
Free-Video
Insights into Mathematics

How to Set Up Fractions IV - The Relation Between Fractions and Other Number Systems

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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.
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6 Lesons
30 minutes
On-Demand
Free-Video
Insights into Mathematics

Measurement, Approximation and Interval Arithmetic - Real Numbers and Limits Math Foundations

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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.
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10 Lesons
42 minutes
On-Demand
Free-Video
Insights into Mathematics

Measurement, Approximation and Interval Arithmetic - Real Numbers and Limits Math Foundations

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Explores interval arithmetic for natural numbers and integers, covering definitions, inequalities, arithmetic operations, and applications in measurement and counting. Lays foundations for mathematical reasoning.
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10 Lesons
46 minutes
On-Demand
Free-Video
Insights into Mathematics

The Division Algorithm for Polynumbers - Arithmetic + Geometry Math Foundations | N J Wildberger

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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.
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9 Lesons
45 minutes
On-Demand
Free-Video
Insights into Mathematics

Extending Arithmetic to Infinity - Real Numbers and Limits Math Foundations

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Explore extending arithmetic to infinity using rational numbers and projective geometry. Learn about integral points, theorems, and distributive laws in this mathematical journey.
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10 Lesons
32 minutes
On-Demand
Free-Video
Insights into Mathematics

Fractions and the Stern-Brocot Tree - Real Numbers and Limits Math Foundations

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Explore the Stern-Brocot tree, a fascinating representation of fractions using a binary tree. Learn its properties, construction, and connections to Ford circles and Farey sequences in this insightful mathematical journey.
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10 Lesons
36 minutes
On-Demand
Free-Video
Insights into Mathematics

The Deep Structure of the Rational Numbers - Real Numbers and Limits Math Foundations

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Explores the deep structure of rational numbers, focusing on their layered nature within [0,1]. Covers key concepts like Farey sequences and Ford circles, emphasizing rationals' importance in modern mathematics.
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10 Lesons
36 minutes
On-Demand
Free-Video
Michael Penn

Do We Even Need the Real Numbers?

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Explore the possibility of calculus using only rational numbers and discover the crucial role of the axiom of completeness in fundamental calculus theorems.
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1 Lesons
26 minutes
On-Demand
Free-Video
Michael Penn

Real Analysis - The Countability of the Rational Numbers

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Explore a rigorous proof demonstrating the countability of rational numbers using a unique approach of representing them as a countable union of disjoint finite sets in real analysis.
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5 Lesons
21 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Conway's Tangles by Michael Lacey

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Explore Conway's method of tangling ropes, associating each tangle with a rational number. Learn how twists and rotations create tangles, and discover their remarkable additive properties through interactive demonstrations.
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1 Lesons
50 minutes
On-Demand
Free-Video
Insights into Mathematics

How to Set Up Fractions - Famous Math Problems 24

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Rigorous exploration of fraction theory, covering fundamental operations, comparisons, proofs, and arithmetic laws. Emphasizes the importance of robust number systems in mathematics.
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9 Lesons
24 minutes
On-Demand
Free-Video
Insights into Mathematics

Visualizing Decimal Numbers and Their Arithmetic - MathFoundations 67

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Explore decimal numbers as special rational numbers, their visualization on a number line, and arithmetic operations. Learn precise definitions and unique properties of decimals in mathematics.
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12 Lesons
44 minutes
On-Demand
Free-Video
Insights into Mathematics

Rational Curvature of a Polytope - Algebraic Topology Lecture 15

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Introduces a new rational definition of polytope curvature, using turn-angle to connect curvature with Euler number. Explores opposite cones and applies Harriot's theorem on spherical triangles.
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1 Lesons
50 minutes
On-Demand
Free-Video
Insights into Mathematics

Pure and Applied Geometry - Understanding the Continuum - Universal Hyperbolic Geometry 20

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Explores the distinction between pure and applied geometry, challenging traditional views on real numbers and the continuum. Offers a rational number-based approach to understanding geometric concepts and continuums.
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10 Lesons
39 minutes
On-Demand
Free-Video
Insights into Mathematics

Mathematical Space and Basic Duality in Geometry - Rational Geometry Math Foundations 122

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Exploring fundamental concepts of mathematical space, including the duality between affine and projective views, Cartesian geometry, and the relationship between affine and projective lines.
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1 Lesons
33 minutes
On-Demand
Free-Video
Insights into Mathematics

Axiomatics and the Least Upper Bound Property in Real Numbers - Math Foundations 121

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Explores flaws in axiomatics for real numbers, examines rational number structure, and introduces the least upper bound property, challenging conventional mathematical foundations.
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1 Lesons
28 minutes
On-Demand
Free-Video
Insights into Mathematics

Difficulties with Dedekind Cuts - Real Numbers and Limits in Mathematics

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Explores challenges in Dedekind's approach to real numbers, questioning the effectiveness of cuts in establishing a logical foundation for real number theory and arithmetic.
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7 Lesons
40 minutes
On-Demand
Free-Video
Insights into Mathematics

Real Numbers as Cauchy Sequences - Limitations and Challenges - Math Foundations 114

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Explores logical weaknesses in using Cauchy sequences to define real numbers, challenging traditional approaches and highlighting ambiguities in fundamental mathematical concepts.
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13 Lesons
52 minutes
On-Demand
Free-Video
Insights into Mathematics

Real Numbers and Cauchy Sequences of Rationals - Math Foundations 111

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Explores Cauchy sequences of rational numbers as a foundation for real numbers, discussing limits, equivalence classes, and the logical challenges in this approach to constructing the real number system.
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7 Lesons
21 minutes
On-Demand
Free-Video
Insights into Mathematics

The Rational Number Line and Irrationalities - Famous Math Problems 19b

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Geometric approach to modeling the continuum using the rational number line. Explores properties, projective view, and introduces irrationalities through Euclidean geometry and polynomial equations.
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7 Lesons
38 minutes
On-Demand
Free-Video
Insights into Mathematics

The Most Fundamental Problem in Mathematics - Famous Math Problems 19a

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Explore the fundamental problem of modeling the continuum in mathematics, examining its historical significance, practical applications, and implications for various mathematical areas.
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9 Lesons
44 minutes
On-Demand
Free-Video
Insights into Mathematics

Inequalities and Limits in Real Numbers - Math Foundations 107

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Simplified epsilon-delta limit definition for rational polynumbers, with visual interpretation and practical examples. Comprehensive review of inequalities for natural numbers, integers, and rational numbers.
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10 Lesons
35 minutes
On-Demand
Free-Video
Insights into Mathematics

Rational Number Arithmetic with Infinity - Extended Rational Numbers and Limits

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Explore arithmetic operations on integral points, extended rational numbers, and the intriguing concept of 0/0. Gain insights into projective geometry and homogeneous coordinates in this mathematical journey.
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10 Lesons
37 minutes
On-Demand
Free-Video
Insights into Mathematics

What Is a Sequence? - Real Numbers and Limits in Mathematics

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Explore the mathematical concept of sequences, from basic definitions to complex examples. Learn about natural numbers, primes, and rational numbers in sequence form, with insights on specification and description.
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7 Lesons
27 minutes
On-Demand
Free-Video
Insights into Mathematics

Central Polynumbers and SL(2)/SU(2) Characters - Math Foundations 235

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Explore a novel algebraic approach to SL(2) and SU(2) representation theory, emphasizing central polynumbers and mset arithmetic, with implications for Lie theory and modern physics.
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6 Lesons
35 minutes
On-Demand
Free-Video
Math with Mr. J

Rational Numbers and Number Lines - Identifying, Graphing, Comparing, and Ordering

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Comprehensive guide to identifying, graphing, comparing, and ordering rational numbers on number lines. Ideal for beginners and those seeking a refresher on these fundamental mathematical concepts.
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5 Lesons
41 minutes
On-Demand
Free-Video
Wrath of Math

Where This Deadly Proof Falls Apart - Analyzing the Irrationality of sqrt(2)

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Explore the classic proof of sqrt(2)'s irrationality and discover its limitations when applied to rational numbers in this insightful mathematical analysis.
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1 Lesons
20 minutes
On-Demand
Free-Video
Schmid College, Chapman University

The Congruent Number Problem

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Explore the ancient congruent number problem and its connection to the Birch and Swinnerton-Dyer conjecture, one of mathematics' most challenging millennium problems.
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1 Lesons
1 hour 23 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Modularity of Abelian Surfaces

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Explorez la preuve de la modularité d'une proportion positive de surfaces abéliennes sur les rationnels dans cette conférence mathématique avancée.
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1 Lesons
1 hour 8 minutes
On-Demand
Free-Video
Banach Center

C*-Bundles Containing the Effros-Shen Algebras

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Explore C*-bundles containing Effros-Shen algebras, examining homeomorphisms, rational numbers, and continuous fractions in this advanced mathematical lecture.
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9 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

The Markov Ordering of the Rationals

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Explore hyperbolic geometry's role in characterizing monotonicity of rational number ordering on a modular torus, connecting to Diophantine approximation and number theory.
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1 Lesons
54 minutes
On-Demand
Free-Video
Paul G. Allen School

PLSE Seminar Series - The Power of Symbolic Automata

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Explores symbolic automata, their applications in program verification, and novel decision procedures for equivalence checking and minimization of these powerful automata operating over infinite alphabets.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
CppNow

Durable Integer Arithmetic

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Exploring integer arithmetic in C++: hardware vs. language rules, challenges for numerical libraries, and potential improvements for more durable and efficient implementations.
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1 Lesons
1 hour 29 minutes
On-Demand
Free-Video
Wrath of Math

Understanding Decimal Expansions - Why Some Numbers Repeat and Others Don't

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Uncover the mathematical principles behind decimal patterns, exploring why certain fractions create repeating decimals while others terminate, through prime factorization and irrational numbers.
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7 Lesons
13 minutes
On-Demand
Free-Video