Oskar Perron, a German mathematician, introduced Perron's paradox to illustrate the danger of assuming the existence of a solution to an optimisation problem. The paradox works like this:

Let \( n \) be the largest positive integer. Then either \( n = 1 \) or \( n \gt 1 \). If \( n \gt 1 \), then \( n^2 \gt n \), contradicting the definition of \( n \). Hence \( n = 1 \).

We get this absurd result because of the incorrect assumption that there exists an integer that is the largest of all the integers.