{ localUrl: '../page/mapsto_notation.html', arbitalUrl: 'https://arbital.com/p/mapsto_notation', rawJsonUrl: '../raw/3vm.json', likeableId: '0', likeableType: 'page', myLikeValue: '0', likeCount: '0', dislikeCount: '0', likeScore: '0', individualLikes: [], pageId: 'mapsto_notation', edit: '8', editSummary: '', prevEdit: '7', currentEdit: '8', wasPublished: 'true', type: 'wiki', title: 'Mapsto notation', clickbait: 'There's an arrow called \\mapsto in LaTeX. What does it mean? ', textLength: '790', alias: 'mapsto_notation', externalUrl: '', sortChildrenBy: 'likes', hasVote: 'false', voteType: '', votesAnonymous: 'false', editCreatorId: 'KevinClancy', editCreatedAt: '2016-07-23 14:44:19', pageCreatorId: 'QiaochuYuan', pageCreatedAt: '2016-05-27 18:24:06', 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: '51', text: 'In mathematics, the arrow $\\mapsto$ (which in [LaTeX] is called "\\mapsto") is used to describe what a [3jy function] does to an arbitrary input. It is commonly used in combination with [3vl colon-to notation], which describes what a function's [3js domain] and [3lg codomain] are. \n\nBy itself, $\\mapsto$ can be used to describe a function without naming it, and so is a way to describe [anonymous_function anonymous functions] in mathematics. \n\n# Examples\n\nThe function $f(x) = x^2$ from the [4bc real numbers] to the real numbers can be described using a combination of colon-to notation and mapsto notation as\n\n$$f : \\mathbb{R} \\to \\mathbb{R}$$\n$$x \\mapsto x^2.$$\n\nIn one line, although this is less common,\n\n$$f : \\mathbb{R} \\ni x \\mapsto x^2 \\in \\mathbb{R}.$$\n\n(see [3vq in notation]). 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It is commonly used in combination with [3vl colon-to notation], which describes what a function's [3js domain] and [3lg codomain] are.' }, creatorIds: [ 'QiaochuYuan', 'EricRogstad', 'KevinClancy' ], childIds: [], parentIds: [ 'LaTeX' ], commentIds: [], questionIds: [], tagIds: [], relatedIds: [], markIds: [], explanations: [], learnMore: [ { id: '5594', parentId: 'mapsto_notation', childId: 'mapsto_notation', type: 'subject', creatorId: 'KevinClancy', createdAt: '2016-07-23 14:43:53', level: '2', isStrong: 'false', everPublished: 'true' } ], requirements: [ { id: '5595', parentId: 'function', childId: 'mapsto_notation', type: 'requirement', creatorId: 'KevinClancy', createdAt: '2016-07-23 14:44:08', level: '2', isStrong: 'true', everPublished: 'true' } ], subjects: [ { id: '5594', parentId: 'mapsto_notation', childId: 'mapsto_notation', type: 'subject', creatorId: 'KevinClancy', createdAt: '2016-07-23 14:43:53', level: '2', isStrong: 'false', everPublished: 'true' } ], lenses: [], 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