Frankl's union-closed sets conjecture

Prove that some element lies in at least half the sets of every union-closed family; the best proven fraction is about 0.38.

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1	{
2	"domain": "mathematics",
3	"topics": [
4	"combinatorics"
5	],
6	"type": "proof",
7	"also": [
8	"construction"
9	],
10	"source": {
11	"key": "optimization-constants",
12	"name": "Optimization Constants in Mathematics",
13	"url": "https://teorth.github.io/optimizationproblems/constants/6a.html",
14	"id": "6",
15	"curator": "Terence Tao and contributors",
16	"poser": "Péter Frankl",
17	"status": "open",
18	"as_of": "2026-10-20",
19	"catalog": "0521c19bbd38"
20	},
21	"review": true,
22	"approval": "first-time"
23	}