{
  localUrl: '../page/transitive_relation.html',
  arbitalUrl: 'https://arbital.com/p/transitive_relation',
  rawJsonUrl: '../raw/573.json',
  likeableId: '0',
  likeableType: 'page',
  myLikeValue: '0',
  likeCount: '0',
  dislikeCount: '0',
  likeScore: '0',
  individualLikes: [],
  pageId: 'transitive_relation',
  edit: '2',
  editSummary: '',
  prevEdit: '1',
  currentEdit: '2',
  wasPublished: 'true',
  type: 'wiki',
  title: 'Transitive relation',
  clickbait: 'If a is related to b and b is related to c, then a is related to c.',
  textLength: '488',
  alias: 'transitive_relation',
  externalUrl: '',
  sortChildrenBy: 'likes',
  hasVote: 'false',
  voteType: '',
  votesAnonymous: 'false',
  editCreatorId: 'MartinEpstein',
  editCreatedAt: '2016-12-19 03:28:20',
  pageCreatorId: 'DylanHendrickson',
  pageCreatedAt: '2016-07-07 17:20:30',
  seeDomainId: '0',
  editDomainId: 'AlexeiAndreev',
  submitToDomainId: '0',
  isAutosave: 'false',
  isSnapshot: 'false',
  isLiveEdit: 'true',
  isMinorEdit: 'false',
  indirectTeacher: 'false',
  todoCount: '0',
  isEditorComment: 'false',
  isApprovedComment: 'true',
  isResolved: 'false',
  snapshotText: '',
  anchorContext: '',
  anchorText: '',
  anchorOffset: '0',
  mergedInto: '',
  isDeleted: 'false',
  viewCount: '65',
  text: 'A binary [-3nt] $R$ is **transitive** if whenever $aRb$ and $bRc$, $aRc$. \n\nThe most common examples or transitive relations are [3rb partial orders] (if $a \\leq b$ and $b \\leq c$, then $a \\leq c$) and [53y equivalence relations] (if $a \\sim b$ and $b \\sim c$, then $a \\sim c$).\n\nA transitive relation that is also [5dy reflexive] is called a [-preorder].\n\nA [-transitive_set] $S$ is a set on which the element-of relation $\\in$ is transitive; whenever $a \\in x$ and $x \\in S$, $a \\in S$.',
  metaText: '',
  isTextLoaded: 'true',
  isSubscribedToDiscussion: 'false',
  isSubscribedToUser: 'false',
  isSubscribedAsMaintainer: 'false',
  discussionSubscriberCount: '0',
  maintainerCount: '0',
  userSubscriberCount: '0',
  lastVisit: '',
  hasDraft: 'false',
  votes: [],
  voteSummary: 'null',
  muVoteSummary: '0',
  voteScaling: '0',
  currentUserVote: '-2',
  voteCount: '0',
  lockedVoteType: '',
  maxEditEver: '0',
  redLinkCount: '0',
  lockedBy: '',
  lockedUntil: '',
  nextPageId: '',
  prevPageId: '',
  usedAsMastery: 'false',
  proposalEditNum: '0',
  permissions: {
    edit: {
      has: 'false',
      reason: 'You don't have domain permission to edit this page'
    },
    proposeEdit: {
      has: 'true',
      reason: ''
    },
    delete: {
      has: 'false',
      reason: 'You don't have domain permission to delete this page'
    },
    comment: {
      has: 'false',
      reason: 'You can't comment in this domain because you are not a member'
    },
    proposeComment: {
      has: 'true',
      reason: ''
    }
  },
  summaries: {},
  creatorIds: [
    'DylanHendrickson',
    'MartinEpstein'
  ],
  childIds: [],
  parentIds: [
    'relation_mathematics'
  ],
  commentIds: [
    '70f'
  ],
  questionIds: [],
  tagIds: [
    'formal_definition_meta_tag',
    'stub_meta_tag'
  ],
  relatedIds: [],
  markIds: [],
  explanations: [],
  learnMore: [],
  requirements: [],
  subjects: [],
  lenses: [],
  lensParentId: '',
  pathPages: [],
  learnMoreTaughtMap: {},
  learnMoreCoveredMap: {},
  learnMoreRequiredMap: {},
  editHistory: {},
  domainSubmissions: {},
  answers: [],
  answerCount: '0',
  commentCount: '0',
  newCommentCount: '0',
  linkedMarkCount: '0',
  changeLogs: [
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '20989',
      pageId: 'transitive_relation',
      userId: 'MartinEpstein',
      edit: '2',
      type: 'newEdit',
      createdAt: '2016-12-19 03:28:20',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '3019',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '1',
      dislikeCount: '0',
      likeScore: '1',
      individualLikes: [],
      id: '16186',
      pageId: 'transitive_relation',
      userId: 'JoeZeng',
      edit: '0',
      type: 'newTag',
      createdAt: '2016-07-08 15:35:57',
      auxPageId: 'formal_definition_meta_tag',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '16009',
      pageId: 'transitive_relation',
      userId: 'DylanHendrickson',
      edit: '0',
      type: 'newTag',
      createdAt: '2016-07-07 17:21:12',
      auxPageId: 'stub_meta_tag',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '16008',
      pageId: 'transitive_relation',
      userId: 'DylanHendrickson',
      edit: '0',
      type: 'newParent',
      createdAt: '2016-07-07 17:20:32',
      auxPageId: 'relation_mathematics',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '16006',
      pageId: 'transitive_relation',
      userId: 'DylanHendrickson',
      edit: '1',
      type: 'newEdit',
      createdAt: '2016-07-07 17:20:30',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    }
  ],
  feedSubmissions: [],
  searchStrings: {},
  hasChildren: 'false',
  hasParents: 'true',
  redAliases: {},
  improvementTagIds: [],
  nonMetaTagIds: [],
  todos: [],
  slowDownMap: 'null',
  speedUpMap: 'null',
  arcPageIds: 'null',
  contentRequests: {}
}