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#Real Numbers

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University of Chicago Department of Mathematics

Spectra and Definability in Combinatorial Sets of Reals

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Dive into the intricacies of spectra and definability in set theory with Vera Fischer's exploration of combinatorial sets of reals and cardinal characteristics of the continuum.
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1 Lesons
55 minutes
On-Demand
Free-Video

Sequences

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Explore fundamental concepts of sequences, including limits, convergence, and advanced topics like limsup and the Bolzano Weierstraß Theorem. Gain a deep understanding of mathematical analysis.
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48 Lesons
10 hours
On-Demand
Free-Video
The Bright Side of Mathematics

Start Learning Mathematics

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Comprehensive introduction to mathematical foundations, covering logic, set theory, number systems, real numbers, and complex numbers with a focus on rigorous definitions and proofs.
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30 Lesons
4 hours 30 minutes
On-Demand
Free-Video

PreAlgebra

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Master fundamental pre-algebra concepts: real numbers, integers, exponents, order of operations, factors, fractions, and basic algebraic expressions and equations. Gain essential math skills for future studies.
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25 Lesons
2 hours 30 minutes
On-Demand
Free-Video

Algebra 1

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Master fundamental algebraic concepts: real numbers, equations, inequalities, exponents, polynomials, and factoring. Develop problem-solving skills and build a strong foundation for advanced mathematics.
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21 Lesons
3 hours 30 minutes
On-Demand
Free-Video

Algebra 1 - Unit 2

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Comprehensive exploration of real numbers, covering addition, subtraction, multiplication, and division, with focus on integers, negative numbers, and algebraic concepts like distributive property and like terms.
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22 Lesons
1 hour 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
Wrath of Math

What Numbers Satisfy This Inequality? - IMO 1962 Problem 2

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Detailed solution to IMO 1962 Problem 2, exploring a complex square root inequality through mathematical analysis, intermediate value theorem, and algebraic manipulation.
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7 Lesons
27 minutes
On-Demand
Free-Video
CIMPA UCR

Algunos Resultados Recientes en Expansiones Beta

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Explora la teoría de expansiones beta en números reales, su relación con la dinámica y los avances recientes en expansiones únicas y simétricas.
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1 Lesons
57 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

Logical Difficulties With the Modern Theory of Limits - Real Numbers + Limits Math Foundations

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Explores logical issues with the modern theory of limits in mathematics, examining the formal definition and its problems through examples and historical context.
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6 Lesons
36 minutes
On-Demand
Free-Video
Insights into Mathematics

Emile Borel - Real Number Enthusiast or Skeptic? - Sociology and Pure Mathematics

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Explore Emile Borel's contributions to measure theory and his skepticism about real numbers, including normal numbers and the intriguing concept of a "know-it-all" number.
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5 Lesons
24 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

The Stern-Brocot Tree, Matrices and Wedges - Real Numbers and Limits Math Foundations

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Explore the Stern-Brocot tree's matrix and geometric representations, including wedges, for a deeper understanding of fractions and their relationships in mathematics.
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10 Lesons
34 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
Insights into Mathematics

Problems with Limits and Cauchy Sequences - Real Numbers and Limits Math Foundations

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Explores challenges in defining real numbers using Cauchy sequences, discussing convergence concepts and visualizing sequences in the plane. Highlights issues in establishing arithmetic for real numbers.
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8 Lesons
29 minutes
On-Demand
Free-Video
Insights into Mathematics

Difficulties With Real Numbers as Infinite Decimals - Real Numbers + Limits Math Foundations

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Explores challenges in defining real numbers as infinite decimals from a computational perspective, highlighting technical obstacles in algorithms, arithmetic operations, and number equality recognition.
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13 Lesons
52 minutes
On-Demand
Free-Video
Insights into Mathematics

Fractions and Repeating Decimals - Real Numbers and Limits Math Foundations

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Explore fractions, repeating decimals, and real numbers. Learn conversion algorithms, arithmetic operations, and gain insights into the foundations of mathematics and rational number theory.
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12 Lesons
49 minutes
On-Demand
Free-Video
Insights into Mathematics

The Decline of Rigour in Modern Mathematics - Real Numbers and Limits

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Explores the decline of mathematical rigor, discussing Euclid's Elements, proof concepts, and problematic topics in modern mathematics. Examines reasons for this decline and its impact on mathematical foundations.
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8 Lesons
27 minutes
On-Demand
Free-Video
Fields Institute

Numerical Computation of Monodromy Action Over R

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Explore numerical computation of monodromy action over real numbers, focusing on a new piece-wise approach for analyzing real solution sets, with applications in kinematics and mechanism calibration.
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8 Lesons
37 minutes
On-Demand
Free-Video
Apna Teacher

Maths - System of Real Numbers, Exponents & Radicals

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Comprehensive coverage of real numbers, exponents, and radicals for 9th and 10th grade math, including detailed explanations and exercises to build strong foundational skills.
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27 Lesons
3 hours 30 minutes
On-Demand
Free-Video
The Royal Institution

The Story of Mathematical Proof - From Ancient Greece to Modern Logic

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Explore the evolution of mathematical proof across number theory, geometry, topology, and logic, delving into the fascinating gap between natural and real numbers.
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18 Lesons
44 minutes
On-Demand
Free-Video
Insights into Mathematics

Difficulties with Real Numbers as Infinite Decimals - Part 1

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Explores challenges in defining real numbers as infinite decimals, examining advantages and drawbacks of the infinite choice approach, and discussing historical debates on arithmetic laws and mathematical foundations.
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10 Lesons
51 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

A Socratic Look at Logical Weaknesses in Modern Pure Mathematics

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Exploring logical weaknesses in pure mathematics, focusing on continuum, analysis, and set theory. Challenges conventional understanding of limits and introduces computational thinking perspectives.
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13 Lesons
52 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

Axiomatics and the Least Upper Bound Property in Real Numbers - Math Foundations 120

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Explores the shifting meaning of axioms in mathematics and its impact on real number theory, challenging traditional views on mathematical foundations.
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1 Lesons
29 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

The Mostly Absent Theory of Real Numbers - Math Foundations 115

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Explores flaws in standard treatments of real numbers in calculus and analysis textbooks, challenging conventional thinking and advocating for a more rigorous mathematical foundation.
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1 Lesons
52 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 113

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Explore Archimedean real numbers and Cauchy sequences, examining their definitions, properties, and applications in mathematical analysis and approximation theory.
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6 Lesons
30 minutes
On-Demand
Free-Video
Insights into Mathematics

Real Numbers and Cauchy Sequences of Rationals - Math Foundations 112

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Explores the concept of real numbers, challenging their existence and examining how quantities like length, area, and function values are inherently approximate rather than exact 'real' values.
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8 Lesons
36 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

Dedekind Cuts and Computational Difficulties with Real Numbers - Famous Math Problems 19

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Explores the challenges and misconceptions surrounding 'real numbers', examining various approaches like infinite decimals, Dedekind cuts, and Cauchy sequences, while emphasizing the importance of concrete computations in mathematics.
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1 Lesons
1 hour 10 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

The Magic and Mystery of Pi - Real Numbers and Limits

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Explore the history, formulas, and philosophical implications of pi, from ancient calculations to modern computations, challenging traditional views on its nature and role in mathematics.
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11 Lesons
42 minutes
On-Demand
Free-Video
Insights into Mathematics

Cracking the Riemann Hypothesis - A Computational Approach

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Explore a computational approach to the Riemann Hypothesis, challenging traditional mathematical assumptions and proposing a new perspective on this famous conjecture.
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1 Lesons
28 minutes
On-Demand
Free-Video
Wolfram

Math Storytelling: Calculus and Beyond - Part Two

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Explore calculus and advanced mathematical concepts with Stephen Wolfram in this engaging continuation of his math storytelling series, delving into symbols, real numbers, and integral forms.
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9 Lesons
2 hours 38 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Real and Complex Number Systems - Lecture 1

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Explore real and complex numbers, their properties, and applications in mathematical analysis and problem-solving.
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1 Lesons
25 minutes
On-Demand
Free-Video
TabletClass Math

Finding Distance on a Number Line - How Far is A to B?

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Aprende a calcular distancias en una recta numérica real mediante pasos hacia adelante y hacia atrás. Domina conceptos fundamentales de matemáticas aplicables a diversas situaciones.
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1 Lesons
15 minutes
On-Demand
Free-Video
Schmid College, Chapman University

Frege's Definition of Real Numbers is Consistent

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Explore Frege's consistent definition of real numbers as ratios of magnitudes. Uncover how slight modifications to his original work could have preserved this groundbreaking mathematical concept.
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1 Lesons
1 hour 50 minutes
On-Demand
Free-Video
Schmid College, Chapman University

Revised GCH or Would Cantor Have Understood - A Contemporary Perspective on the Continuum Hypothesis

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Explore the Continuum Hypothesis and its philosophical implications in set theory. Examine contemporary perspectives on Cantor's famous postulate and its generalized form.
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1 Lesons
1 hour 39 minutes
On-Demand
Free-Video
Schmid College, Chapman University

Remarks about Cantor's Theorem

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Explore Cantor's Theorem and its implications for infinite cardinalities. Examine the historical context, compare proofs, and discover applications to paradoxical mathematical situations.
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1 Lesons
1 hour 13 minutes
On-Demand
Free-Video
Simons Institute

Low Degree Testing over the Reals

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Explore low degree testing over real numbers, focusing on theoretical concepts and applications in local algorithms.
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1 Lesons
33 minutes
On-Demand
Free-Video
NCCR SwissMAP

Introduction to Indeterminism in Physics and Intuitionistic Mathematics

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Explore indeterminism in physics and intuitionistic mathematics with Professor Nicolas Gisin, delving into classical chaos and Bohmian mechanics.
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1 Lesons
58 minutes
On-Demand
Free-Video
Kolmogorov-Seminar

Erdos Problem About Bad Denominators and Its Combinatorial Solution

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Delve into a fascinating mathematical exploration of rational approximations, combining number theory with word combinatorics to solve Erdos' problem of finding numbers resistant to specific denominators.
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1 Lesons
2 hours
On-Demand
Free-Video
Michael Penn

Understanding Sequence Convergence - A Mathematical Analysis

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Explore mathematical sequence convergence through step-by-step problem-solving and clear explanations of limit concepts and analytical techniques.
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1 Lesons
18 minutes
On-Demand
Free-Video