{ localUrl: '../page/5n8.html', arbitalUrl: 'https://arbital.com/p/5n8', rawJsonUrl: '../raw/5n8.json', likeableId: '0', likeableType: 'page', myLikeValue: '0', likeCount: '0', dislikeCount: '0', likeScore: '0', individualLikes: [], pageId: '5n8', edit: '1', editSummary: '', prevEdit: '0', currentEdit: '1', wasPublished: 'true', type: 'comment', title: '"This is a clear explanation, but I think some f..."', clickbait: '', textLength: '728', alias: '5n8', externalUrl: '', sortChildrenBy: 'recentFirst', hasVote: 'false', voteType: '', votesAnonymous: 'false', editCreatorId: 'EricRogstad', editCreatedAt: '2016-07-29 19:25:35', pageCreatorId: 'EricRogstad', pageCreatedAt: '2016-07-29 19:25:35', 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 first requirement effectively states both that the distance from an element to itself is 0, and that the distance between non\\-identical elements must be greater than 0\\. The second requirement asserts that a metric must be commutative; informally the distance from $a$ to $b$ must be the same as the distance from $b$ to $a$\\. Finally, the third requirement is known as the triangle inequality and asserts that the distance from $a$ to $c$ is at most as large as the sum of the distances from $a$ to $b$ and from $b$ to $c$\\. It is named as such because in Euclidean space, the points $a$, $b$, and $c$ form a triangle, and the inequality requires that the length of one side of the triangle is not longer than the sum of the lengths of the other two sides; violating this would mean that the shortest path between two points is no longer the straight line between them\\.', anchorText: 'The first requirement effectively states both that the distance from an element to itself is 0, and that the distance between non\\-identical elements must be greater than 0\\. The second requirement asserts that a metric must be commutative; informally the distance from $a$ to $b$ must be the same as the distance from $b$ to $a$\\. Finally, the third requirement is known as the triangle inequality and asserts that the distance from $a$ to $c$ is at most as large as the sum of the distances from $a$ to $b$ and from $b$ to $c$\\. It is named as such because in Euclidean space, the points $a$, $b$, and $c$ form a triangle, and the inequality requires that the length of one side of the triangle is not longer than the sum of the lengths of the other two sides; violating this would mean that the shortest path between two points is no longer the straight line between them\\.', anchorOffset: '0', mergedInto: '', isDeleted: 'false', viewCount: '126', text: 'This is a clear explanation, but I think some formatting changes could enable readers to grok it even more quickly.\n\nSuppose a reader understands two of the three requirements and just needs an explanation of the third. It would be cool if they could find the sentences they're looking for w/o having to scan a whole paragraph looking for the words, "first", "second", or "third".\n\nI think we can achieve this by A) moving each explanation right under the equation / inequality it's talking about, or B) putting the three explanations in a second numbered list, or C) leaving the three explanations in a paragraph, but use the numerals 1, 2, and 3 within the paragraph. Might require some experimentation to see what looks best.', metaText: '', isTextLoaded: 'true', isSubscribedToDiscussion: 'false', isSubscribedToUser: 'false', isSubscribedAsMaintainer: 'false', discussionSubscriberCount: '2', maintainerCount: '2', 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: [ 'EricRogstad' ], childIds: [], parentIds: [ 'metric' ], commentIds: [ '5pq' ], 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: '17732', pageId: '5n8', userId: 'EricRogstad', edit: '1', type: 'newEdit', createdAt: '2016-07-29 19:25:35', auxPageId: '', oldSettingsValue: '', newSettingsValue: '' } ], feedSubmissions: [], searchStrings: {}, hasChildren: 'false', hasParents: 'true', redAliases: {}, improvementTagIds: [], nonMetaTagIds: [], todos: [], slowDownMap: 'null', speedUpMap: 'null', arcPageIds: 'null', contentRequests: {} }