Berry's paradox

Imagine you have a basket of berries. You count the number of berries in the basket. Let's say there are 10 berries. You write on a piece of paper, "the number of berries in this basket is greater than any number that can be written in English using fewer than twenty words." This is a paradox because you just wrote a sentence using only eleven words that describes a number that is supposedly greater than any number that can be described using fewer than twenty words.

It's like saying, "I can run faster than anyone who has ever run before." How do you know that for sure? It's impossible to prove. In the case of Berry's paradox, the sentence you wrote contradicts itself because it describes a number that can't exist. It's like trying to make a square circle or a hot ice cube. They just can't exist.

So although it seems like a simple statement, it's actually a paradox because it creates a contradiction. The number of berries in the basket can't possibly be greater than any number that can be written in English using fewer than twenty words. And that's Berry's paradox in a nutshell!