Zeno’s Paradox

Zeno’s paradox begins like this:
In order for a man to reach another, he needs to cover half the distance first. After that, he needs to cover the next quarter of the distance. Thereafter, he needs to cover the next eighth of the distance, and so on. With these small increments that he has to cover, as it is seemingly infinite, will the man never get to anywhere?

Here is the fascinating answer.

First, we realise that 1 can be split up into infinite parts – 1=\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+...

Hence an infinite parts can also be added up to 1 – \dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+...=1

Therefore, even though the man needs to walk an infinite number of fractions to get to his destination, he will still get there.

And here is the mind-blowing nature of \infty.