> The sentence “Let x⋆ be the solution to the optimization problem” implicitly asserts that the solution is unique. If the solution is not unique or need
not be unique, write, “Let x⋆ be a solution to the optimization problem.”
I know this point is meant to be about precision in writing but this reminded me of Perron's Paradox, which highlights the danger of assuming the existence of a solution without proper justification. The problem can be demonstrated through the following argument:
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.
This fallacy arises from the mistaken assumption that a largest integer exists in the first place.
The original post is a great submission, by the way. Thank you for sharing it on HN. Bookmarked already!
I know this point is meant to be about precision in writing but this reminded me of Perron's Paradox, which highlights the danger of assuming the existence of a solution without proper justification. The problem can be demonstrated through the following argument:
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.
This fallacy arises from the mistaken assumption that a largest integer exists in the first place.
The original post is a great submission, by the way. Thank you for sharing it on HN. Bookmarked already!