{ localUrl: '../page/natural_number.html', arbitalUrl: 'https://arbital.com/p/natural_number', rawJsonUrl: '../raw/45h.json', likeableId: '2654', likeableType: 'page', myLikeValue: '0', likeCount: '1', dislikeCount: '0', likeScore: '1', individualLikes: [ 'EricRogstad' ], pageId: 'natural_number', edit: '11', editSummary: '', prevEdit: '10', currentEdit: '11', wasPublished: 'true', type: 'wiki', title: 'Natural number', clickbait: 'The numbers we use to count: 0, 1, 2, 3, ...', textLength: '1592', alias: 'natural_number', externalUrl: '', sortChildrenBy: 'likes', hasVote: 'false', voteType: '', votesAnonymous: 'false', editCreatorId: 'MartinEpstein', editCreatedAt: '2016-12-22 06:39:50', pageCreatorId: 'JaimeSevillaMolina', pageCreatedAt: '2016-06-12 08:43:34', seeDomainId: '0', editDomainId: 'AlexeiAndreev', submitToDomainId: '0', isAutosave: 'false', isSnapshot: 'false', isLiveEdit: 'true', isMinorEdit: 'false', indirectTeacher: 'false', todoCount: '1', isEditorComment: 'false', isApprovedComment: 'true', isResolved: 'false', snapshotText: '', anchorContext: '', anchorText: '', anchorOffset: '0', mergedInto: '', isDeleted: 'false', viewCount: '83', text: '[summary: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ...\n\nThe natural numbers are the numbers we use to count things.]\n\nA **natural number** is a number like 0, 1, 2, 3, 4, 5, 6, ... which can be used to represent the count of an object. The set of natural numbers is $\\mathbb N.$ Not all sources include 0 in $\\mathbb N.$\n\nNatural numbers are perhaps the simplest type of number. They don't include [48l negative numbers], [4zq fractional numbers], [4bc irrational numbers], [4zw imaginary numbers], or any of those complexities.\n\nThanks to their simplicity, natural numbers are often the first mathematical concept taught to children. Natural numbers are equipped with a notion of [-addition] ($2 + 3 = 5$ and so on) and [-multiplication] ($2 \\cdot 3 = 6$ and so on), these are among the first mathematical operations taught to children.\n\nDespite their simplicity, the natural numbers are a ubiquitous and useful mathematical object. They're quite useful for counting things. They represent all the possible [4w5 cardinalities] of finite [3jz sets]. They're also a useful [data_structure data structure], in that numbers can be used to [numeric_encoding encode] all sorts of data. Almost all of modern mathematics can be built out of natural numbers.\n\n[todo: Add a "formalization" lens with the Peano axioms. I recommend at least one page with just the raw Peano axioms (and very little prose), and another gentler introduction sort of like http://bit.ly/29glDrR and http://bit.ly/29nKYAL, albeit more to-the-point and probably without going all the way up to non-standard number territory.]', 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: 'true', 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: [ 'JoeZeng', 'PatrickStevens', 'NateSoares', 'JaimeSevillaMolina', 'EricRogstad', 'MartinEpstein' ], childIds: [ 'grahams_number', 'googolplex', 'googol', 'prime_number' ], parentIds: [ 'math' ], commentIds: [], questionIds: [], tagIds: [ 'start_meta_tag', 'definition_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: '3859', likeableType: 'changeLog', myLikeValue: '0', likeCount: '1', dislikeCount: '0', likeScore: '1', individualLikes: [], id: '21050', pageId: 'natural_number', userId: 'MartinEpstein', edit: '11', type: 'newEdit', createdAt: '2016-12-22 06:39:50', auxPageId: '', oldSettingsValue: '', newSettingsValue: '' }, { likeableId: '0', likeableType: 'changeLog', myLikeValue: '0', likeCount: '0', dislikeCount: '0', likeScore: '0', individualLikes: [], id: '19037', pageId: 'natural_number', userId: 'JoeZeng', edit: '0', type: 'deleteChild', createdAt: '2016-08-20 15:44:33', auxPageId: 'natural_number_numbersets', oldSettingsValue: '', newSettingsValue: '' }, { likeableId: '0', likeableType: 'changeLog', myLikeValue: '0', likeCount: '0', dislikeCount: '0', likeScore: '0', individualLikes: [], id: '19009', pageId: 'natural_number', userId: 'EricBruylant', edit: '0', type: 'newChild', createdAt: '2016-08-20 13:20:45', auxPageId: 'grahams_number', oldSettingsValue: '', newSettingsValue: '' }, { likeableId: '0', likeableType: 'changeLog', myLikeValue: '0', likeCount: '0', dislikeCount: '0', likeScore: '0', individualLikes: [], id: '18971', pageId: 'natural_number', userId: 'EricBruylant', edit: '0', type: 'newChild', createdAt: '2016-08-20 13:03:23', auxPageId: 'googolplex', oldSettingsValue: '', newSettingsValue: '' }, { likeableId: '0', likeableType: 'changeLog', myLikeValue: '0', likeCount: '0', dislikeCount: '0', likeScore: '0', individualLikes: [], id: '18967', pageId: 'natural_number', userId: 'EricBruylant', edit: '0', type: 'newChild', createdAt: '2016-08-20 13:03:07', auxPageId: 'googol', oldSettingsValue: '', newSettingsValue: '' }, { likeableId: '3010', likeableType: 'changeLog', myLikeValue: '0', likeCount: '1', dislikeCount: '0', likeScore: '1', individualLikes: [], id: '16102', pageId: 'natural_number', userId: 'JoeZeng', edit: '10', type: 'newEdit', createdAt: '2016-07-07 23:38:29', auxPageId: '', oldSettingsValue: '', newSettingsValue: '' }, { likeableId: '0', likeableType: 'changeLog', myLikeValue: '0', likeCount: '0', dislikeCount: '0', likeScore: '0', individualLikes: [], id: '15695', pageId: 'natural_number', userId: 'JoeZeng', edit: '9', type: 'newEdit', createdAt: '2016-07-06 15:06:27', auxPageId: '', oldSettingsValue: '', newSettingsValue: '' }, { likeableId: '0', likeableType: 'changeLog', myLikeValue: '0', likeCount: '0', dislikeCount: '0', likeScore: '0', individualLikes: [], id: '15672', pageId: 'natural_number', userId: 'JoeZeng', edit: '8', type: 'newEdit', createdAt: '2016-07-06 14:50:49', auxPageId: '', oldSettingsValue: '', newSettingsValue: 'Try not to use "whole number" anywhere; 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