subtraction
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.
Bundle → Layer → Finding → Questions Filled
4 bundles · 8 layers · 8 findings · 16 questions
Understand What subtraction is.
Definition
Definition.
Definition
Definition.
- What is subtraction, and how does it differ from negation, set difference, division and absolute difference? definition
- Is the question about arithmetic, teaching, vectors or computing? boundary
Vectors
Vector subtraction.
Vectors
Vectors.
- How is vector subtraction done geometrically and by components? definition
- Which entry fits Euclidean vector? action
Methods Methods.
Algorithms
Written algorithms.
Algorithms
Algorithms.
- How do borrowing and equal additions methods work? provenance
- Which references are standard? provenance
Teaching
Teaching strategies.
Teaching
Teaching.
- How do teachers use counting up and number lines for subtraction? provenance
- Which sources are cited? provenance
Computing Computing.
Complements
Two s complement.
Complements
Complements.
- How does two s complement turn subtraction into addition? provenance
- Which entry fits two s complement? action
Floating point
Cancellation.
Floating point
Floating point.
- What is catastrophic cancellation in floating-point subtraction? provenance
- Which entry fits floating-point arithmetic? action
Context History.
Negative numbers
Negative numbers.
Negative numbers
Negative numbers.
- How did subtraction lead to acceptance of negative numbers? provenance
- Which entry fits negative number? action
Minus sign
Minus sign history.
Minus sign
Minus sign.
- When did the minus sign appear in print? provenance
- Which entry fits plus and minus signs? action
Classifiers Filled
- Family
- Thing Registry
- Category
- Cross-cutting context
- Entry kind
- thing
- Plane
- XCT
- Domain
- XCT.QLT
- Other names and narrower kinds
- vector subtraction
What it is Filled
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.
Why it exists Filled
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.
Distinguishing features Filled
- Inverse of addition
- Not commutative
- Can yield negatives
- Extends to vectors
What robots and AI may and may not do Filled
Must not
- 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.
Only with a human decision
- Correcting subtraction errors in financial or dosing records that others rely on.
May
- Perform and explain subtraction, including with negative numbers.
- Check results and point out sign errors and cancellation errors in calculations.
Moral aspects Filled
- Small arithmetic errors in money or medicine can harm people downstream.
- Teaching arithmetic patiently matters to people who struggle with it.
Who is affected
- Learners
- People relying on calculations
Owners Filled
Steward
Nobody owns it; it is part of mathematics held in common.
Links to other meta-models Filled
parent
- Q164307 - registry parent class
related
- binary operation - in registry terms
- addition
- vector subtraction
- set difference
What else AI and robots need to interact with it Filled
Identity and identifiers required Filled
- Vercy registry: vr.tr.subtraction
- Wikidata: Q40754 (https://www.wikidata.org/wiki/Q40754)
Direct properties not applicable Not applicable
- terms: minuend, subtrahend, difference list
- minus sign in print: 1489 year - Widmann, as commonly cited
- two s complement: standard in computers note
Plane XCT: no invented physical properties.
Recognition optional Filled
- 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 and actions required Filled
- explain properties and terms
- relay algorithms and teaching methods
- describe vector subtraction
- distinguish related operations
Hazards and failure modes required Filled
- Assuming commutativity
- Sign errors with negatives
- Floating-point cancellation errors
Standards and interfaces required Filled
- ISO 80000-2 notation
- National mathematics curricula
Context of use required Filled
- Finding differences and removing quantities.
- whole number subtraction
- integer and real subtraction
- vector and matrix subtraction
- modular subtraction
- binary subtraction
Sources Filled
- Wikidata item Q40754: subtraction - identity and sense of the item
- Wikipedia: Subtraction - general description of the item
Open questions
- Should vector subtraction be a separate entry?
- How should mathematics education sources be linked?
- Should binary subtraction be linked?
Machine files
Provenance
thing registry research (pass 2) · unreviewed
Built from: models/things/publications/thing-q40754/spec.json