- Gorakhpur University Syllabus
- D. ALEMBERT’s Test of Convergence of Series
- The Lindemann Theory of Unimolecular Reactions
- Statistical Physics: Ensembles
- Dedekind’s Theory of Real Numbers
- Set Theory, Functions and Real Number System
- Statistical Physics: Macrostates and Microstates
- 5 Average Students Who Aced IIT with Flying Colors
- 8 big online communities a math major should join
- The Area of a Disk
- Solving Integral Equations

## Smart Fallacies: i=1, 1= 2 and 1= 3

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}$ and $ \sqrt{1}=1$ , we can have $ \dfrac{i}{1}=\dfrac{1}{i} \ldots \{1 \}$ $ \Rightarrow i^2=1 \ldots \{2 \}$ . This is complete contradiction to the…