{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.function","code":"thing-q11348","url":"https://ver.cy/models/thing/q11348/","name":"function","alternateNames":[],"kind":"thing","status":"published","version":"0.2.0-wave.1","language":"en","classifiers":{"family":"Thing Registry","category":"Cross-cutting context","entryKind":"thing","plane":"XCT","domain":["XCT.QLT"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"In mathematics, a relation that assigns to each element of a set (the domain) exactly one element of another set (the codomain).","purpose":"Let an agent handle functions by domain, codomain, rule and properties, and distinguish mathematical functions from programming functions and biological functions.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Each input has exactly one output","Defined with domain and codomain","Partial functions leave some inputs undefined","Properties include injective, surjective, bijective"],"structure":{"bundles":[{"id":"definition","name":"Definition","description":"Domain and rule.","layers":[{"id":"domain","name":"Domain and codomain","description":"Sets.","findings":[{"id":"domain-finding","name":"Domain","description":"Domain and codomain.","questions":[{"text":"What are the domain and codomain?","kind":"definition"},{"text":"Is it defined for all inputs?","kind":"boundary"}]}]},{"id":"rule","name":"Rule","description":"How outputs are computed.","findings":[{"id":"rule-finding","name":"Rule","description":"Defining rule.","questions":[{"text":"What rule defines it?","kind":"definition"},{"text":"Is it given by formula, table or algorithm?","kind":"definition"}]}]}]},{"id":"properties","name":"Properties","description":"Behaviour.","layers":[{"id":"mapping","name":"Mapping properties","description":"Injective, surjective.","findings":[{"id":"mapping-finding","name":"Mapping","description":"Mapping properties.","questions":[{"text":"Is it injective, surjective or bijective?","kind":"measurement"},{"text":"Does it have an inverse?","kind":"boundary"}]}]},{"id":"analysis","name":"Analytic properties","description":"Continuity, differentiability.","findings":[{"id":"analysis-finding","name":"Analysis","description":"Analytic properties.","questions":[{"text":"Is it continuous and differentiable?","kind":"measurement"},{"text":"Where not?","kind":"boundary"}]}]}]},{"id":"representation","name":"Representation","description":"Graphs and code.","layers":[{"id":"graph","name":"Graph","description":"Plot.","findings":[{"id":"graph-finding","name":"Graph","description":"Graph.","questions":[{"text":"What does its graph look like?","kind":"definition"},{"text":"What are its key features?","kind":"measurement"}]}]},{"id":"computation","name":"Computation","description":"Evaluation.","findings":[{"id":"computation-finding","name":"Computation","description":"Numerical evaluation.","questions":[{"text":"How can it be evaluated accurately?","kind":"action"},{"text":"Where is it numerically unstable?","kind":"boundary"}]}]}]},{"id":"use","name":"Use","description":"Modelling.","layers":[{"id":"model","name":"Model","description":"Applications.","findings":[{"id":"model-finding","name":"Model","description":"Modelling use.","questions":[{"text":"What relationship does it model?","kind":"definition"},{"text":"How well does it fit data?","kind":"measurement"}]}]},{"id":"senses","name":"Other senses","description":"Programming and biology.","findings":[{"id":"senses-finding","name":"Senses","description":"Disambiguation.","questions":[{"text":"Is the mathematical sense meant?","kind":"boundary"},{"text":"Which other entry fits better?","kind":"action"}]}]}]}]},"agentConduct":{"may":["Define, compute and analyse functions.","Explain function concepts to learners."],"mustNot":["Misstate a function's domain or properties in a proof or calculation.","Present an unverified proof as correct.","Claim credit for others' mathematical work."],"requiresHuman":["Using mathematical results in safety-critical systems."]},"ethics":{"considerations":["Mathematical errors can propagate into critical systems.","Credit for results matters to mathematicians."],"affectedParties":["Students","Users of mathematical results"]},"owners":{"steward":"Nobody owns a mathematical concept; 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sense: Wikidata description; 2 live sources; review by codex: pass","interaction.properties":"Plane XCT: no invented physical properties."},"score":1.0}}