{ localUrl: '../page/4hr.html', arbitalUrl: 'https://arbital.com/p/4hr', rawJsonUrl: '../raw/4hr.json', likeableId: '0', likeableType: 'page', myLikeValue: '0', likeCount: '0', dislikeCount: '0', likeScore: '0', individualLikes: [], pageId: '4hr', edit: '1', editSummary: '', prevEdit: '0', currentEdit: '1', wasPublished: 'true', type: 'comment', title: '"I understand what you're sa..."', clickbait: '', textLength: '827', alias: '4hr', externalUrl: '', sortChildrenBy: 'recentFirst', hasVote: 'false', voteType: '', votesAnonymous: 'false', editCreatorId: 'KevinClancy', editCreatedAt: '2016-06-17 15:16:54', pageCreatorId: 'KevinClancy', pageCreatedAt: '2016-06-17 15:16:54', 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: '191', text: 'I understand what you're saying and I think it's a good point. The problem is that you're developing an algorithm (a non-terminating one) that finds real numbers rather than providing a definition of them. It turns out that providing a definition of real numbers is not a simple as it may at first seem. This presentation is somewhat similar constructive analysis, in which a real number is defined as regularly converging sequence of rational numbers; importantly, constructive analysis does not define real numbers as *infinite sums* of these sequences, because as I've said, that would be a circular definition.\n\nIf you want to learn more about rigorous foundations for real numbers and related topics, I think that the book Calculus by Michael Spivak is a very approachable and well respected introduction to the topic. ', 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: [ 'KevinClancy' ], childIds: [], parentIds: [ 'real_number', '4h5' ], 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: '13539', pageId: '4hr', userId: 'KevinClancy', edit: '1', type: 'newEdit', createdAt: '2016-06-17 15:16:54', auxPageId: '', oldSettingsValue: '', newSettingsValue: '' }, { likeableId: '0', likeableType: 'changeLog', myLikeValue: '0', likeCount: '0', dislikeCount: '0', likeScore: '0', individualLikes: [], id: '13532', pageId: '4hr', userId: 'KevinClancy', edit: '1', type: 'newParent', createdAt: '2016-06-17 15:09:12', auxPageId: 'real_number', oldSettingsValue: '', newSettingsValue: '' }, { likeableId: '0', likeableType: 'changeLog', myLikeValue: '0', likeCount: '0', dislikeCount: '0', likeScore: '0', individualLikes: [], id: '13533', pageId: '4hr', userId: 'KevinClancy', edit: '1', type: 'newParent', createdAt: '2016-06-17 15:09:12', auxPageId: '4h5', oldSettingsValue: '', newSettingsValue: '' } ], feedSubmissions: [], searchStrings: {}, hasChildren: 'false', hasParents: 'true', redAliases: {}, improvementTagIds: [], nonMetaTagIds: [], todos: [], slowDownMap: 'null', speedUpMap: 'null', arcPageIds: 'null', contentRequests: {} }