Insights What is a Real Number? A 5 Minute Introduction

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Real numbers can be defined through two primary methods: Cauchy sequences and Dedekind cuts. Both approaches highlight the complexity behind defining what seems like a simple concept. The Cauchy sequence method requires an understanding of equivalence classes to fully grasp its implications. This discussion emphasizes that a rigorous mathematical foundation is necessary for a proper definition of real numbers. Understanding these concepts is essential for deeper mathematical studies.
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There are two main ways to introduce real numbers. Cauchy sequences are one possibility, Dedekind cuts are another. It is surprising how such a for us common thing like real numbers need some elaborated mathematics in order to properly define them. Even the approach by Cauchy sequences needs the concept of equivalence classes.
 

Thread 'Leibniz Rule Videos on Digital-University'

Good morning I have been refreshing my memory about Leibniz differentiation of integrals and found some useful videos from digital-university.org on YouTube. Although the audio quality is poor and the speaker proceeds a bit slowly, the explanations and processes are clear. However, it seems that one video in the Leibniz rule series is missing. While the videos are still present on YouTube, the referring website no longer exists but is preserved on the internet archive...
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