# Difference between revisions of "Frankl's union-closed conjecture"

A family $\mathcal{A}$ of sets is called union closed if $A\cup B\in\mathcal{A}$ whenever $A\in\mathcal{A}$ and $B\in\mathcal{A}$. Frankl's conjecture is a disarmingly simple one: if $\mathcal{A}$ is a union-closed family of n sets, then must there be an element that belongs to at least n/2 of the sets? The problem has been open for decades, despite the attention of several people.
{"ft_lang_label":"__label__en","ft_lang_prob":0.8577792,"math_prob":0.9964389,"size":828,"snap":"2020-10-2020-16","text_gpt3_token_len":261,"char_repetition_ratio":0.16626213,"word_repetition_ratio":0.0,"special_character_ratio":0.2741546,"punctuation_ratio":0.071428575,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9843808,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-04-01T02:21:51Z\",\"WARC-Record-ID\":\"<urn:uuid:a6acf5c7-1824-4ac9-a8a3-cb868c09e781>\",\"Content-Length\":\"15211\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:923a4e0a-f060-4f3d-a61b-3261c6088edb>\",\"WARC-Concurrent-To\":\"<urn:uuid:9ba675c8-3f5d-4254-9324-e9fab20c2835>\",\"WARC-IP-Address\":\"64.90.49.117\",\"WARC-Target-URI\":\"http://michaelnielsen.org/polymath1/index.php?title=Frankl%27s_union-closed_conjecture&oldid=9784&diff=prev\",\"WARC-Payload-Digest\":\"sha1:2USIXJWGKHRWEHW36D7GUBVGTRFCIYCK\",\"WARC-Block-Digest\":\"sha1:PHBB5MGSMN2ZUYT5FSABOT73E62XCOVF\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-16/CC-MAIN-2020-16_segments_1585370505359.23_warc_CC-MAIN-20200401003422-20200401033422-00510.warc.gz\"}"}