Real Analysis

This mathematical fallacy is due to a simple assumption, that $ -1=\dfrac{-1}{1}=\dfrac{1}{-1}$ . Proceeding with $ \dfrac{-1}{1}=\dfrac{1}{-1}$ and taking square-roots of both sides, we get: $ \dfrac{\sqrt{-1}}{\sqrt{1}}=\dfrac{\sqrt{1}}{\sqrt{-1}}$ Now, as the Euler’s constant $ i= \sqrt{-1}$

Last year, I managed to successfully finish Metric Spaces, Basic Topology and other Analysis topics. Starting from the next semester I’ll be learning more pure mathematical topics, like Functional Analysis, Combinatorics and more. The plan