Understanding the Essence of Calculus — Part II

This is the 2nd part of this article on “Understanding the Essence of Calculus”.If you have not read it, then check out the 1st part of this article from here .

4. What leads to the idea of LIMITS

Before jumping into “what is limits ? ” it is better to know what drives mathematicians to derive the concept of limits and for that we need to again go back to very ancient times of Greece where a philosopher named “Zino” who had been working on some paradoxes which keeps him thinking how to get out of those paradoxes. Ok Let’s start from the beginning….

Zeno of Elea, an ancient Greek Philosopher famous for inventing number of paradoxes, where arguments that seem logical, but whose conclusion is illogical or contradictory. One of the best known is the “Zeno’s dichotomy paradox”, which means “the paradox of cutting in two” in Ancient Greek.

What is this Dichotomy Paradox:

After a hectic day at work Zeno decides to take a walk from his house to a park to get some fresh air. In order to clear to get to the park, he firsts has to get to the half of the way to the park. This take some finite amount of time, once he gets to half way from his house he needs to walk to half the remaining distance.Again, this takes a finite amount of…