{ localUrl: '../page/5g9.html', arbitalUrl: 'https://arbital.com/p/5g9', rawJsonUrl: '../raw/5g9.json', likeableId: '3138', likeableType: 'page', myLikeValue: '0', likeCount: '1', dislikeCount: '0', likeScore: '1', individualLikes: [ 'KevinClancy' ], pageId: '5g9', edit: '1', editSummary: '', prevEdit: '0', currentEdit: '1', wasPublished: 'true', type: 'comment', title: '"I really like this domino analogy.\n\nAlso, I'd e..."', clickbait: '', textLength: '440', alias: '5g9', externalUrl: '', sortChildrenBy: 'recentFirst', hasVote: 'false', voteType: '', votesAnonymous: 'false', editCreatorId: 'EricRogstad', editCreatedAt: '2016-07-17 21:04:23', pageCreatorId: 'EricRogstad', pageCreatedAt: '2016-07-17 21:04:23', 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 principle of mathematical induction is a proof technique in which a statement, $P(n)$, is proven about a set of natural numbers $n$\\. It may be best understood as treating the statements like dominoes: a statement $P(n)$ is true if the $n$\\-th domino is knocked down\\. We must knock down a first domino, or prove that a base case $P(m)$ is true\\. Next we must make sure the dominoes are close enough together to fall, or that the inductive step holds; in other words, we prove that if $k \\geq m$ and $P(k)$ is true, $P(k+1)$ is true\\. Then since $P(m)$ is true, $P(m+1)$ is true; and since $P(m+1)$ is true, $P(m+2)$ is true, and so on\\.', anchorText: 'It may be best understood as treating the statements like dominoes', anchorOffset: '138', mergedInto: '', isDeleted: 'false', viewCount: '291', text: 'I really like this domino analogy.\n\nAlso, I'd expect to see the word "all" somewhere in this first paragraph -- I think it's worth emphasizing the point that if we have the base case and the inductive step then the statement will be true for *all* of the numbers after the base case, just like all of the dominoes after the first one would fall down. I think the current final sentence of the intro paragraph doesn't make this clear enough.', 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: [ 'EricRogstad' ], childIds: [], parentIds: [ 'mathematical_induction' ], 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: '17057', pageId: '5g9', userId: 'EricRogstad', edit: '1', type: 'newEdit', createdAt: '2016-07-17 21:04:23', auxPageId: '', oldSettingsValue: '', newSettingsValue: '' } ], feedSubmissions: [], searchStrings: {}, hasChildren: 'false', hasParents: 'true', redAliases: {}, improvementTagIds: [], nonMetaTagIds: [], todos: [], slowDownMap: 'null', speedUpMap: 'null', arcPageIds: 'null', contentRequests: {} }