{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.limit","code":"thing-q177239","url":"https://ver.cy/models/thing/q177239/","name":"limit","alternateNames":["set-theoretic limit","mutation limit","Cesaro summation","liability limit","maximum residue limit","limit of a function","control limit","resolution limit","engineering tolerance","limit from below","limit from above","critical value"],"kind":"thing","status":"published","version":"0.2.0-wave.2","language":"en","classifiers":{"family":"Thing Registry","category":"Cross-cutting context","entryKind":"thing","plane":"XCT","domain":["XCT.QLT"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"In mathematics, the value that a function or sequence approaches as the input or index approaches some value or infinity, defined rigorously by epsilon-delta and related definitions and underpinning continuity, derivatives, integrals and series, with extensions such as set-theoretic limits and summation methods; outside mathematics the word denotes a boundary or maximum, as in speed limits, liability limits and residue limits.","purpose":"Let an agent explain and compute mathematical limits, explain their rigorous definition and role, and separate the everyday and regulatory senses of limit.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Value approached","Rigorous definition","Foundation of calculus","Homonym with bounds and rules"],"structure":{"bundles":[{"id":"compute","name":"Compute","description":"Finding limits.","layers":[{"id":"evaluate","name":"Evaluate","description":"Evaluating a limit.","findings":[{"id":"evaluate-finding","name":"Evaluate","description":"Evaluation.","questions":[{"text":"What is the limit of this function or sequence, and which technique shows it?","kind":"measurement"},{"text":"Does the limit exist, and are one-sided limits equal?","kind":"boundary"}]}]},{"id":"indeterminate","name":"Indeterminate","description":"Indeterminate forms.","findings":[{"id":"indeterminate-finding","name":"Indeterminate","description":"Indeterminate forms.","questions":[{"text":"How are indeterminate forms resolved, for example by algebra or the rule of l Hopital?","kind":"action"},{"text":"When does the rule apply?","kind":"boundary"}]}]}]},{"id":"define","name":"Define","description":"Rigorous definition.","layers":[{"id":"epsilon","name":"Epsilon","description":"Formal definition.","findings":[{"id":"epsilon-finding","name":"Epsilon","description":"Formal definition.","questions":[{"text":"What is the epsilon-delta definition of this limit, and how is it used in a proof?","kind":"definition"},{"text":"How does the sequence definition differ?","kind":"definition"}]}]},{"id":"role","name":"Role","description":"Role in calculus.","findings":[{"id":"role-finding","name":"Role","description":"Role.","questions":[{"text":"How do limits define continuity, derivatives, integrals and series?","kind":"definition"},{"text":"Why were limits introduced historically?","kind":"provenance"}]}]}]},{"id":"advanced","name":"Advanced","description":"Generalisations.","layers":[{"id":"sets","name":"Sets","description":"Set-theoretic limits.","findings":[{"id":"sets-finding","name":"Sets","description":"Set limits.","questions":[{"text":"What are the limit superior and inferior of a sequence of sets or numbers?","kind":"definition"},{"text":"Where are they used?","kind":"provenance"}]}]},{"id":"summation","name":"Summation","description":"Summation methods.","findings":[{"id":"summation-finding","name":"Summation","description":"Summation methods.","questions":[{"text":"What does Cesaro summation assign to a divergent series, and how does it relate to limits?","kind":"definition"},{"text":"When are such methods legitimate?","kind":"boundary"}]}]}]},{"id":"senses","name":"Senses","description":"Other senses.","layers":[{"id":"regulatory","name":"Regulatory","description":"Limits as rules.","findings":[{"id":"regulatory-finding","name":"Regulatory","description":"Regulatory limits.","questions":[{"text":"Is a regulatory or contractual limit meant, such as a speed, liability or residue limit?","kind":"boundary"},{"text":"Which entry or authority applies?","kind":"action"}]}]},{"id":"teach","name":"Teach","description":"Teaching limits.","findings":[{"id":"teach-finding","name":"Teach","description":"Teaching.","questions":[{"text":"How can limits be taught intuitively before formalising?","kind":"action"},{"text":"Which misconceptions arise?","kind":"provenance"}]}]}]}]},"agentConduct":{"may":["Compute and explain limits, including the epsilon-delta definition.","Say when a limit does not exist or depends on direction."],"mustNot":["Report a limit that does not exist as having a value.","Use infinite or limiting arguments carelessly in results others rely on.","Present intuitive explanations as rigorous proof."],"requiresHuman":["Using limit-based approximations in a calculation that is signed off for safety."]},"ethics":{"considerations":["Precise reasoning about limits prevents errors in science and engineering.","Clear teaching helps learners who find the concept difficult."],"affectedParties":["Students","Engineers and scientists"]},"owners":{"steward":"Nobody owns the concept; it is held in common by mathematics.","roles":[],"masterSystems":[]},"relations":[{"target":"Q13222579","type":"parent","note":"registry parent class"},{"target":"Q24034552","type":"parent","note":"registry parent class"},{"target":"mathematical concept","type":"related","note":"category"},{"target":"upper and lower bounds","type":"related","note":"category"},{"target":"mathematical analysis","type":"related","note":"field"},{"target":"integral","type":"related","note":"definition"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.limit","Wikidata: Q177239 (https://www.wikidata.org/wiki/Q177239)"]},"properties":{"applicability":"not-applicable","items":[]},"recognition":{"applicability":"optional","items":["lim notation","Approach to a value","A bound is not necessarily a limit","Not physical; notation and definitions."]},"capabilities":{"applicability":"required","items":["compute limits of functions and sequences","explain the rigorous definition","explain the role of limits in calculus","separate regulatory and everyday senses"]},"hazards":{"applicability":"required","items":["Treating limits as values reached","Ignoring one-sided differences","Confusing senses"]},"interfaces":{"applicability":"required","items":["ISO 80000-2 notation","Regulatory limits are governed by domain-specific rules"]},"context":{"applicability":"required","items":["Foundations of calculus and analysis.","limits of sequences","limits of functions","one-sided and infinite limits","set-theoretic limits and summation methods","limits in the sense of bounds and rules (separate sense)"]}},"sources":[{"title":"Wikidata item Q177239: limit","url":"https://www.wikidata.org/wiki/Q177239","note":"identity and sense of the item"},{"title":"Wikipedia: Limit (mathematics)","url":"https://en.wikipedia.org/wiki/Limit_%28mathematics%29","note":"general description of the item"}],"openQuestions":["Should sequence and function limits be separate entries?","How should teaching resources be linked?","How should regulatory senses be split?"],"resources":{"spec":"/models/things/publications/thing-q177239/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q177239/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-11T19:59:16Z","builder":"tools/build_cards.py@1.0.0"},"completeness":{"sections":{"classifiers":"filled","whatItIs":"filled","purpose":"filled","distinguishingFeatures":"filled","structure":"filled","agentConduct":"filled","ethics":"filled","owners":"filled","relations":"filled","interaction.identity":"filled","interaction.properties":"not-applicable","interaction.recognition":"filled","interaction.capabilities":"filled","interaction.hazards":"filled","interaction.interfaces":"filled","interaction.context":"filled","sources":"filled"},"notes":{"_gate":"Published through the thing publication gate 1.0 on 2026-10-06T19:51:55+00:00: completeness 1.00; sense: Wikidata description; 2 live sources; review by codex: pass","interaction.properties":"Plane XCT: no invented physical properties."},"score":1.0}}