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 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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