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Claim. S. L. G. Choi, The largest sum-free subsequence from a sequence of $n$ numbers, Proc. Amer. Math. Soc. 39 (1973), no. 1, 42--44. As the zbMATH review (Zbl 0248.10041) states it: for the largest $g(n)$ such that any sequence of $n$ real numbers has a subsequence of $g(n)$ numbers none of which is the sum of other numbers of the subsequence, the paper proves, by a method different from Erdős's,

$$g(n)>\tfrac{35}{36}n^{1/2}\qquad(n\ge n_0),$$

improving Erdős's $g(n)>2^{-1/2}n^{1/2}$. Sets of integers are sets of real numbers, so the bound holds for the site's $l(n)$ of Problem 790. The paper is not held, and Erdős's 1973 survey (printed p. 130) gives the constant differently, reporting Choi's improvement as $l(n)>(1+c)\sqrt n$, a form the site repeats; the 1975 paper of Choi, Komlós and Szemerédi lists the paper as its reference 2 without restating the bound. The constant above is the review's; the paper itself would settle which form it proves.

Covers. A lower bound $l(n)\gg n^{1/2}$ with a constant larger than Erdős's $2^{-1/2}$, $35/36$ as the review gives it, for all large $n$. Not covered: the first displayed question, which the 1975 Theorem answers, and the second.

Depends on. No page of this wiki.

Acceptance. Refereed: the paper appeared in the Proceedings of the American Mathematical Society, volume 39, no. 1 (June 1973; the Crossref record gives the year only, so this page is named by the first day of the issue's month). The site's curator, Thomas F. Bloom, credits the improvement of Erdős's bound to Choi in the problem page's commentary (label OPEN, page last edited 23 January 2026); the problem is not marked settled there, so the credit is recorded here and is not listed as reviewed. The paper's own text is not checked in this corpus.