{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.subtraction","code":"thing-q40754","url":"https://ver.cy/models/thing/q40754/","name":"subtraction","alternateNames":["vector subtraction"],"kind":"thing","status":"published","version":"0.2.0-wave.4","language":"en","classifiers":{"family":"Thing Registry","category":"Cross-cutting context","entryKind":"thing","plane":"XCT","domain":["XCT.QLT"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"The arithmetic operation of taking one quantity away from another, written a minus b, giving the difference, with a the minuend and b the subtrahend, the inverse of addition, not commutative or associative, extended from natural numbers to integers, rationals, real and complex numbers and to vector subtraction, which subtracts corresponding components or adds the negative vector; methods include borrowing or regrouping, complements used in computers, where two s complement makes subtraction a form of addition, and mental strategies such as counting up.","purpose":"Let an agent explain subtraction, relay properties, algorithms, teaching methods and extensions from mathematics and education sources, describe vector subtraction, and distinguish subtraction from negation, set difference, division and absolute difference.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Inverse of addition","Not commutative","Can yield negatives","Extends to vectors"],"structure":{"bundles":[{"id":"understand","name":"Understand","description":"What subtraction is.","layers":[{"id":"definition","name":"Definition","description":"Definition.","findings":[{"id":"definition-finding","name":"Definition","description":"Definition.","questions":[{"text":"What is subtraction, and how does it differ from negation, set difference, division and absolute difference?","kind":"definition"},{"text":"Is the question about arithmetic, teaching, vectors or computing?","kind":"boundary"}]}]},{"id":"vectors","name":"Vectors","description":"Vector subtraction.","findings":[{"id":"vectors-finding","name":"Vectors","description":"Vectors.","questions":[{"text":"How is vector subtraction done geometrically and by components?","kind":"definition"},{"text":"Which entry fits Euclidean vector?","kind":"action"}]}]}]},{"id":"methods","name":"Methods","description":"Methods.","layers":[{"id":"algorithms","name":"Algorithms","description":"Written algorithms.","findings":[{"id":"algorithms-finding","name":"Algorithms","description":"Algorithms.","questions":[{"text":"How do borrowing and equal additions methods work?","kind":"provenance"},{"text":"Which references are standard?","kind":"provenance"}]}]},{"id":"teaching","name":"Teaching","description":"Teaching strategies.","findings":[{"id":"teaching-finding","name":"Teaching","description":"Teaching.","questions":[{"text":"How do teachers use counting up and number lines for subtraction?","kind":"provenance"},{"text":"Which sources are cited?","kind":"provenance"}]}]}]},{"id":"computing","name":"Computing","description":"Computing.","layers":[{"id":"complement","name":"Complements","description":"Two s complement.","findings":[{"id":"complement-finding","name":"Complements","description":"Complements.","questions":[{"text":"How does two s complement turn subtraction into addition?","kind":"provenance"},{"text":"Which entry fits two s complement?","kind":"action"}]}]},{"id":"float","name":"Floating point","description":"Cancellation.","findings":[{"id":"float-finding","name":"Floating point","description":"Floating point.","questions":[{"text":"What is catastrophic cancellation in floating-point subtraction?","kind":"provenance"},{"text":"Which entry fits floating-point arithmetic?","kind":"action"}]}]}]},{"id":"context","name":"Context","description":"History.","layers":[{"id":"negatives","name":"Negative numbers","description":"Negative numbers.","findings":[{"id":"negatives-finding","name":"Negative numbers","description":"Negative numbers.","questions":[{"text":"How did subtraction lead to acceptance of negative numbers?","kind":"provenance"},{"text":"Which entry fits negative number?","kind":"action"}]}]},{"id":"sign","name":"Minus sign","description":"Minus sign history.","findings":[{"id":"sign-finding","name":"Minus sign","description":"Minus sign.","questions":[{"text":"When did the minus sign appear in print?","kind":"provenance"},{"text":"Which entry fits plus and minus signs?","kind":"action"}]}]}]}]},"agentConduct":{"may":["Perform and explain subtraction, including with negative numbers.","Check results and point out sign errors and cancellation errors in calculations."],"mustNot":["Treat subtraction as commutative or associative.","Hide precision lost by subtracting nearly equal floating-point numbers in critical results.","Present a difference as exact when its inputs were rounded or uncertain."],"requiresHuman":["Correcting subtraction errors in financial or dosing records that others rely on."]},"ethics":{"considerations":["Small arithmetic errors in money or medicine can harm people downstream.","Teaching arithmetic patiently matters to people who struggle with it."],"affectedParties":["Learners","People relying on calculations"]},"owners":{"steward":"Nobody owns it; it is part of mathematics held in common.","roles":[],"masterSystems":[]},"relations":[{"target":"Q164307","type":"parent","note":"registry parent class"},{"target":"binary operation","type":"related","note":"in registry terms"},{"target":"addition","type":"related"},{"target":"vector subtraction","type":"related"},{"target":"set difference","type":"related"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.subtraction","Wikidata: Q40754 (https://www.wikidata.org/wiki/Q40754)"]},"properties":{"applicability":"not-applicable","items":["terms: minuend, subtrahend, difference list","minus sign in print: 1489 year - Widmann, as commonly cited","two s complement: standard in computers note"]},"recognition":{"applicability":"optional","items":["Arithmetic operation of taking away","Vector subtraction, difference, minus","Negation reverses sign; set difference removes elements; division splits into parts; absolute difference ignores order","Not a physical object; written with the minus sign."]},"capabilities":{"applicability":"required","items":["explain properties and terms","relay algorithms and teaching methods","describe vector subtraction","distinguish related operations"]},"hazards":{"applicability":"required","items":["Assuming commutativity","Sign errors with negatives","Floating-point cancellation errors"]},"interfaces":{"applicability":"required","items":["ISO 80000-2 notation","National mathematics curricula"]},"context":{"applicability":"required","items":["Finding differences and removing quantities.","whole number subtraction","integer and real subtraction","vector and matrix subtraction","modular subtraction","binary subtraction"]}},"sources":[{"title":"Wikidata item Q40754: subtraction","url":"https://www.wikidata.org/wiki/Q40754","note":"identity and sense of the item"},{"title":"Wikipedia: Subtraction","url":"https://en.wikipedia.org/wiki/Subtraction","note":"general description of the item"}],"openQuestions":["Should vector subtraction be a separate entry?","How should mathematics education sources be linked?","Should binary subtraction be linked?"],"resources":{"spec":"/models/things/publications/thing-q40754/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q40754/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-13T23:07:57Z","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 2026-10-06T19:51:59+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}}