Sanjoy Nath's Geometric Junction Theory meets Sanjoy Nath's Geometrifying Trigonometry

 hOW MANY PHILOSOPHIES ARE THERE TO CONSTRUCT REAL NUMBERS?????????? That's a great question that gets to the heart of what a "number" even is! There isn't a single, universally accepted count for the number of philosophies for constructing real numbers , as new perspectives continue to emerge. However, the modern mathematical world is built on three primary, foundational approaches: The Dominant Philosophies Dedekind Cuts: This is perhaps the most famous and widely taught philosophy. Developed by Richard Dedekind, it defines a real number by partitioning the set of rational numbers into two non-empty subsets. For example, the square root of 2 is the "cut" that separates all rational numbers whose square is less than 2 from all those whose square is greater than 2. This approach directly gives rise to the idea of the continuous number line, which is why Sanjoy Nath's work is so provocative—it challenges this very foundation. Cauchy Sequences: In this ...