Quotes on Divergent Series

There are so many ways to be brave in this world. Sometimes bravery involves laying down your life for something bigger than yourself, or for someone else. Sometimes it involves giving up everything you have ever known, or everyone you have ever loved, for the sake of something greater. But sometimes it doesn't. Sometimes it is nothing more than gritting your teeth through pain, and the work of every day, the slow walk toward a better life. That is the sort of bravery I must have now.

Notable enough, however, are the controversies over the series 1 - 1 + 1 - 1 + 1 - ... whose sum was given by Leibniz as 1/2, although others disagree. ... Understanding of this question is to be sought in the word "sum"; this idea, if thus conceived - namely, the sum of a series is said to be that quantity to which it is brought closer as more terms of the series are taken - has relevance only for convergent series, and we should in general give up the idea of sum for divergent series.