{
localUrl: '../page/field_structure_of_rational_numbers.html',
arbitalUrl: 'https://arbital.com/p/field_structure_of_rational_numbers',
rawJsonUrl: '../raw/516.json',
likeableId: '0',
likeableType: 'page',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
pageId: 'field_structure_of_rational_numbers',
edit: '2',
editSummary: '',
prevEdit: '1',
currentEdit: '2',
wasPublished: 'true',
type: 'wiki',
title: 'Field structure of rational numbers',
clickbait: 'In which we describe the field structure on the rationals.',
textLength: '839',
alias: 'field_structure_of_rational_numbers',
externalUrl: '',
sortChildrenBy: 'likes',
hasVote: 'false',
voteType: '',
votesAnonymous: 'false',
editCreatorId: 'PatrickStevens',
editCreatedAt: '2016-07-29 20:39:26',
pageCreatorId: 'PatrickStevens',
pageCreatedAt: '2016-07-03 16:50:59',
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: '91',
text: 'The [4zq rational numbers], being the [-field_of_fractions] of the [48l integers], have the following [481 field] structure:\n\n- Addition is given by $\\frac{a}{b} + \\frac{p}{q} = \\frac{aq+bp}{bq}$\n- Multiplication is given by $\\frac{a}{b} \\frac{c}{d} = \\frac{ac}{bd}$\n- The identity under addition is $\\frac{0}{1}$\n- The identity under multiplication is $\\frac{1}{1}$\n- The additive inverse of $\\frac{a}{b}$ is $\\frac{-a}{b}$\n- The multiplicative inverse of $\\frac{a}{b}$ (where $a \\not = 0$) is $\\frac{b}{a}$.\n\nIt additionally inherits a [540 total ordering] which respects the field structure: $0 < \\frac{c}{d}$ if and only if $c$ and $d$ are both positive or $c$ and $d$ are both negative.\nAll other information about the ordering can be derived from this fact: $\\frac{a}{b} < \\frac{c}{d}$ if and only if $0 < \\frac{c}{d} - \\frac{a}{b}$.',
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: [
'PatrickStevens'
],
childIds: [
'arithmetic_of_rational_numbers_math_0'
],
parentIds: [
'rational_number'
],
commentIds: [],
questionIds: [],
tagIds: [
'formal_definition_meta_tag'
],
relatedIds: [],
markIds: [],
explanations: [
{
id: '5727',
parentId: 'field_structure_of_rational_numbers',
childId: 'rationals_form_a_field_math_0',
type: 'subject',
creatorId: 'PatrickStevens',
createdAt: '2016-07-31 11:03:50',
level: '3',
isStrong: 'true',
everPublished: 'true'
}
],
learnMore: [],
requirements: [
{
id: '4725',
parentId: 'rational_number',
childId: 'field_structure_of_rational_numbers',
type: 'requirement',
creatorId: 'PatrickStevens',
createdAt: '2016-07-03 16:47:08',
level: '1',
isStrong: 'false',
everPublished: 'true'
}
],
subjects: [],
lenses: [
{
id: '62',
pageId: 'field_structure_of_rational_numbers',
lensId: 'arithmetic_of_rational_numbers_math_0',
lensIndex: '0',
lensName: 'Math 0',
lensSubtitle: '',
createdBy: '267',
createdAt: '2016-07-03 16:46:49',
updatedBy: '267',
updatedAt: '2016-07-03 16:46:58'
}
],
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: '17829',
pageId: 'field_structure_of_rational_numbers',
userId: 'PatrickStevens',
edit: '0',
type: 'newTeacher',
createdAt: '2016-07-31 12:18:58',
auxPageId: 'rationals_form_a_field_math_0',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '17747',
pageId: 'field_structure_of_rational_numbers',
userId: 'PatrickStevens',
edit: '2',
type: 'newEdit',
createdAt: '2016-07-29 20:39:26',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '15274',
pageId: 'field_structure_of_rational_numbers',
userId: 'EricBruylant',
edit: '0',
type: 'newTag',
createdAt: '2016-07-04 18:10:16',
auxPageId: 'formal_definition_meta_tag',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '15273',
pageId: 'field_structure_of_rational_numbers',
userId: 'EricBruylant',
edit: '0',
type: 'deleteParent',
createdAt: '2016-07-04 18:10:00',
auxPageId: 'math',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '15271',
pageId: 'field_structure_of_rational_numbers',
userId: 'EricBruylant',
edit: '0',
type: 'newParent',
createdAt: '2016-07-04 18:09:59',
auxPageId: 'rational_number',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '15269',
pageId: 'field_structure_of_rational_numbers',
userId: 'EricBruylant',
edit: '0',
type: 'newParent',
createdAt: '2016-07-04 18:09:24',
auxPageId: 'math',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '15193',
pageId: 'field_structure_of_rational_numbers',
userId: 'PatrickStevens',
edit: '0',
type: 'newChild',
createdAt: '2016-07-03 16:51:00',
auxPageId: 'arithmetic_of_rational_numbers_math_0',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '15195',
pageId: 'field_structure_of_rational_numbers',
userId: 'PatrickStevens',
edit: '0',
type: 'newRequirement',
createdAt: '2016-07-03 16:51:00',
auxPageId: 'rational_number',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '15192',
pageId: 'field_structure_of_rational_numbers',
userId: 'PatrickStevens',
edit: '1',
type: 'newEdit',
createdAt: '2016-07-03 16:50:59',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: ''
}
],
feedSubmissions: [],
searchStrings: {},
hasChildren: 'true',
hasParents: 'true',
redAliases: {},
improvementTagIds: [],
nonMetaTagIds: [],
todos: [],
slowDownMap: 'null',
speedUpMap: 'null',
arcPageIds: 'null',
contentRequests: {}
}