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Subjects
Mathematics
Real Numbers

Free Online

Real Numbers Courses and Certifications

Explore the foundations of real numbers, limits, and infinite decimals through rigorous mathematical analysis. Access in-depth video tutorials on YouTube covering Cauchy sequences, decimal representations, and measurement theory, plus structured courses on Coursera and OpenLearn for systematic learning.

148 courses

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The Organic Chemistry Tutor
Real Numbers

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

Explore fundamental concepts of real numbers, limits, and mathematical foundations through critical examination of infinity, sequences, and numerical approximation methods.
- YouTube
- 17 hours 19 minutes
- On-Demand
- Free Video
Insights into Mathematics
Axiomatics and the Least Upper Bound Property in Real Numbers - Math Foundations 120

Explores the shifting meaning of axioms in mathematics and its impact on real number theory, challenging traditional views on mathematical foundations.
- YouTube
- 29 minutes
- On-Demand
- Free Video
Insights into Mathematics
The Mostly Absent Theory of Real Numbers - Math Foundations 115

Explores flaws in standard treatments of real numbers in calculus and analysis textbooks, challenging conventional thinking and advocating for a more rigorous mathematical foundation.
- YouTube
- 52 minutes
- On-Demand
- Free Video
Insights into Mathematics
Real Numbers and Cauchy Sequences of Rationals - Math Foundations 111

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.
- YouTube
- 21 minutes
- On-Demand
- Free Video
Insights into Mathematics
Difficulties with Real Numbers as Infinite Decimals - Part 1

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.
- YouTube
- 51 minutes
- On-Demand
- Free Video
Insights into Mathematics
Problems with Limits and Cauchy Sequences - Real Numbers and Limits Math Foundations

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.
- YouTube
- 29 minutes
- On-Demand
- Free Video
Insights into Mathematics
Difficulties With Real Numbers as Infinite Decimals - Real Numbers + Limits Math Foundations

Explores challenges in defining real numbers as infinite decimals from a computational perspective, highlighting technical obstacles in algorithms, arithmetic operations, and number equality recognition.
- YouTube
- 52 minutes
- On-Demand
- Free Video
Insights into Mathematics
Fractions and Repeating Decimals - Real Numbers and Limits Math Foundations

Explore fractions, repeating decimals, and real numbers. Learn conversion algorithms, arithmetic operations, and gain insights into the foundations of mathematics and rational number theory.
- YouTube
- 49 minutes
- On-Demand
- Free Video
Insights into Mathematics
The Decline of Rigour in Modern Mathematics - Real Numbers and Limits

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.
- YouTube
- 27 minutes
- On-Demand
- Free Video
Insights into Mathematics
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.
- YouTube
- 42 minutes
- On-Demand
- Free Video
Data Science Math Skills
12 reviews

Master essential math concepts for data science: set theory, real numbers, functions, graphs, rates of change, and probability theory. Build a strong foundation for advanced analysis.
- Coursera
- 13 hours 20 minutes
- On-Demand
- Paid Course
NES Mathematics Middle Grades & Early Secondary (105): Practice & Study Guide
1 review

Comprehensive preparation for NES Mathematics exam, covering key topics from mathematical reasoning to geometry and statistics. Bite-sized lessons and quizzes ensure thorough understanding and exam readiness.
- Study.com
- 37 hours
- On-Demand
- Paid Course
Introduction to analysis
3 ratings at OpenLearn

This free course is an introduction to analysis which looks at real numbers and their properties, with a particular emphasis on inequalities. Section 1 starts by revising rational numbers and their...
- OpenLearn
- 16 hours
- On-Demand
- Free Certificate
TabletClass Math
Finding Distance on a Number Line - How Far is A to B?

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.
- YouTube
- 15 minutes
- On-Demand
- Free Video

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