{ localUrl: '../page/5f9.html', arbitalUrl: 'https://arbital.com/p/5f9', rawJsonUrl: '../raw/5f9.json', likeableId: '0', likeableType: 'page', myLikeValue: '0', likeCount: '0', dislikeCount: '0', likeScore: '0', individualLikes: [], pageId: '5f9', edit: '1', editSummary: '', prevEdit: '0', currentEdit: '1', wasPublished: 'true', type: 'comment', title: '"I think that every metric space is dense in its..."', clickbait: '', textLength: '192', alias: '5f9', externalUrl: '', sortChildrenBy: 'recentFirst', hasVote: 'false', voteType: '', votesAnonymous: 'false', editCreatorId: 'KevinClancy', editCreatedAt: '2016-07-16 17:38:02', pageCreatorId: 'KevinClancy', pageCreatedAt: '2016-07-16 17:38:02', seeDomainId: '0', editDomainId: 'AlexeiAndreev', submitToDomainId: '0', isAutosave: 'false', isSnapshot: 'false', isLiveEdit: 'true', isMinorEdit: 'false', indirectTeacher: 'false', todoCount: '0', isEditorComment: 'true', isApprovedComment: 'true', isResolved: 'false', snapshotText: '', anchorContext: 'The rational numbers have a problem that makes them unsuitable for use in calculus — they have "gaps" in them\\. This may not be obvious or even make sense at first, because the rational numbers are dense in themselves — between any two rational numbers you can always find infinitely many other rational numbers\\. How could there be gaps in a set like that? $\\newcommand{\\rats}{\\mathbb{Q}} \\newcommand{\\Ql}{\\rats^\\le} \\newcommand{\\Qr}{\\rats^\\ge} \\newcommand{\\Qls}{\\rats^<} \\newcommand{\\Qrs}{\\rats^>}$\n$\\newcommand{\\set}[1]{\\left\\{#1\\right\\}} \\newcommand{\\sothat}{\\ |\\ }$ ', anchorText: 'rational numbers are dense in themselves', anchorOffset: '177', mergedInto: '', isDeleted: 'false', viewCount: '100', text: 'I think that every metric space is dense in itself. If X is a metric space, then a set E is dense in X whenever every element of X is either a limit point of E *or an element of E* (or both). ', metaText: '', isTextLoaded: 'true', isSubscribedToDiscussion: 'false', isSubscribedToUser: 'false', isSubscribedAsMaintainer: 'false', discussionSubscriberCount: '1', maintainerCount: '1', 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: [ 'KevinClancy' ], childIds: [], parentIds: [ 'real_number_as_dedekind_cut' ], commentIds: [], questionIds: [], tagIds: [], 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: '16881', pageId: '5f9', userId: 'KevinClancy', edit: '1', type: 'newEdit', createdAt: '2016-07-16 17:38:02', auxPageId: '', oldSettingsValue: '', newSettingsValue: '' } ], feedSubmissions: [], searchStrings: {}, hasChildren: 'false', hasParents: 'true', redAliases: {}, improvementTagIds: [], nonMetaTagIds: [], todos: [], slowDownMap: 'null', speedUpMap: 'null', arcPageIds: 'null', contentRequests: {} }