Math Club
Thursday, March 21st, 2019
Time: 5:30 - 6:30 p.m Place: Jeffery Hall 118
Speaker: Ivan Dimitrov (Queen's University)
Title: Why 0.499999999992646 does not equal 12.
Abstract: We will see why
- $\int_{0}^\infty \frac{\sin x}{x} \,dx = \pi/2,$
- $\int_{0}^\infty \frac{\sin x}{x} \cdot \frac{\sin x/3}{x/3}\, dx = \pi/2, $
… and so on all the way to
- $ \int_{0}^\infty \frac{\sin x}{x} \cdot \frac{\sin x/3}{x/3} \cdots \frac{\sin x/13}{x/13}\, dx = \pi/2. $
However,
- $\int_{0}^\infty \frac{\sin x}{x} \cdot \frac{\sin x/3}{x/3} \cdots \frac{\sin x/13}{x/13} \cdot \frac{\sin x/15}{x/15} \,dx < \pi/2.$