# Perron's Paradox

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**Susam Pal**on 10 Apr 2024Oskar 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 \( n > 1. \) If \( n > 1, \) then \( n^2 > n, \)
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.