My teacher recently showed me a rather weird result and I would like to know if he was just tricking me or if he was serious. He showed me that $g=1-1+1-1+1-...=\frac{1}{2}$ Then he said that $s=1+1+1+1+1+1+...=\frac{1}{2}$ as well because when you add $g$ and $s$, the "ones" in the even columns cancel out and the "ones" in the odd columns add up to $2$'s, so you end up with $2+2+2+2+2+...$ you can factor out a two and get the equation: $s+g=2s$ If $g=\frac{1}{2}$, then $s+\frac{1}{2}=2s$ tells us that $s=\frac{1}{2}$ as well.
Where did he trick me?
You can look up "divergent series" for example on wikipedia if you want to see various "sensible" ways to add up divergent series and get a finite answer, e.g. that are compatible with algebraic manipulations. However any possible way that you get a finite answer for a divergent series is just a "trick," and there is no one right answer, because the series doesn't converge in the traditional sense.