{"action":"closed","issue":{"url":"https://api.github.com/repos/FreeCodeCamp/hikes/issues/16","repository_url":"https://api.github.com/repos/FreeCodeCamp/hikes","labels_url":"https://api.github.com/repos/FreeCodeCamp/hikes/issues/16/labels{/name}","comments_url":"https://api.github.com/repos/FreeCodeCamp/hikes/issues/16/comments","events_url":"https://api.github.com/repos/FreeCodeCamp/hikes/issues/16/events","html_url":"https://github.com/FreeCodeCamp/hikes/issues/16","id":124395292,"number":16,"title":"Discrete Mathematics 12: Powerset (All Possible Subsets)","user":{"login":"SEGrooms","id":13191387,"avatar_url":"https://avatars.githubusercontent.com/u/13191387?v=3","gravatar_id":"","url":"https://api.github.com/users/SEGrooms","html_url":"https://github.com/SEGrooms","followers_url":"https://api.github.com/users/SEGrooms/followers","following_url":"https://api.github.com/users/SEGrooms/following{/other_user}","gists_url":"https://api.github.com/users/SEGrooms/gists{/gist_id}","starred_url":"https://api.github.com/users/SEGrooms/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/SEGrooms/subscriptions","organizations_url":"https://api.github.com/users/SEGrooms/orgs","repos_url":"https://api.github.com/users/SEGrooms/repos","events_url":"https://api.github.com/users/SEGrooms/events{/privacy}","received_events_url":"https://api.github.com/users/SEGrooms/received_events","type":"User","site_admin":false},"labels":[{"url":"https://api.github.com/repos/FreeCodeCamp/hikes/labels/02:%20Scripting","name":"02: Scripting","color":"000000"},{"url":"https://api.github.com/repos/FreeCodeCamp/hikes/labels/Math%20for%20Programmers","name":"Math for Programmers","color":"e11d21"}],"state":"closed","locked":false,"assignee":null,"assignees":[],"milestone":null,"comments":0,"created_at":"2015-12-30T20:20:04Z","updated_at":"2016-07-07T17:47:06Z","closed_at":"2016-07-07T17:47:06Z","body":"Hello World! Shawn Grooms here, and I wanted to expand on a concept that we learned in the last video. The topic of this video is on powersets.\r\n\r\n*fancy P* : A powerset is the set of all possible subsets of a given set.\r\ne.g. Let A = {1,2,3}, then P(A) = {Ø, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3}}\r\n\r\nA natural question now arises. How do I know how many elements will be in the powerset? Simple!\r\nIf A is a finite set, then  |P(A)| = 2^ |A|. This has important consequences that are unfortunately too soon to introduce, but will make more sense when we mention relations and introduce the concept of functions.\r\n\r\nChallenge Problems:\r\n- P({0,1,5}) = ?\r\n- P({a,b}) = ?\r\n- P(Ø) = ?\r\n- P({0,{1},{1,2}})\r\n- P({Ø, {Ø}}) = ?\r\n\r\n*********************************************************************************************************\r\nAlthough we won't really use powersets until we reach relations, it is a nice introduction to combinatorics in disguise. The word powerset sounds comical, whereas combinatorics can sounds intimidating."}}
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