## Posts

### Chasing the lightning

Far too often, the scary and the beautiful are not one and the same thing. But in the case of the phenomenon of lightning, I think they are. As much as petrifying an event it is, lightning is also a captivating natural phenomenon. Dark night skies illuminated by bolts of lightning are some of the most stunning sights one can lay one's eyes on. But don't let this beauty pull wool over your eyes: A lightning strike is potentially lethal. In Nepal alone, according to this article from The Kathmandu Post, lightning claims over 100 lives every year.

Lightning can be described as a flare of bright light caused by an electric discharge inside a cloud, between clouds, or between clouds and the ground. Fortunately for us, most lightning events occur within a cloud or among clouds, and lightning strikes – which involve a cloud-to-ground discharge – are relatively rare. An electrostatic phenomenon, lightning takes place as opposite charges separate in a thunderstorm. When the potential …

### Intuitions to why 0! = 1

Thanks in part to its fancy notation, the factorial is something we're all familiar with. For a non-negative integer n, the factorial is the product of all positive integers less than or equal to n. That is, $$n! = n.(n - 1).(n - 2) ... .3.2.1$$ This means that the factorial of the non-negative integer 4, or 4!, is given as $$4! = 4.3.2.1 = 24$$ While the factorial is defined for all non-negative integers, the general rule is such that it is destined to break down for the smallest non-negative integer, which is zero. However, as a matter of convention, we know that 0! equals 1. So why does it?
The key is a property known as the empty product. Just as a sum of no numbers is zero, which is the empty sum, any product of no factors is equal to one. Thus, 0!, which we know is a product for the simple reason that it's a factorial operation, must be equal to unity.

Unlike the result of an empty sum, which is intuitively one, the result of an empty product seems to defy common sense. …