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.