## Math Club - Ivan Dimitrov (Queen's University)

### 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, $