Perron's Paradox

from blog Susam Pal, | ↗ original
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 \( n > 1. \) If \( n > 1, \) then \( n^2 > n, \) contradicting the...