It wasn’t just the Pythagoreans, who had difficulties with the existence of irrational numbers or incommensurable numbers as the Greeks called them in their geometry. Source: Wikimedia CommonsThe Pythagoreans stumbled upon irrational numbers in their comparisons of line segments. However, this step, equivalent to going to the limit in calculus was never even considered as far as we know. Secondly, the method of exhaustion, avoiding infinity, does not have a limit concept. The limit concept is totally central to integral calculus and would, as will see much later in this series, cause several generations of mathematicians a lot of problems.