addition
Let an agent handle addition by domain, properties and methods, from arithmetic to algebraic structures.
Bundle → Layer → Finding → Questions Filled
4 bundles · 8 layers · 8 findings · 16 questions
Domain What is added.
Objects
Numbers, vectors.
Objects
Domain.
- What kind of objects are being added? definition
- How is addition defined for them? definition
Units
Compatible quantities.
Units
Units.
- Are the quantities in the same units? boundary
- How are they converted? action
Properties Laws.
Laws
Commutative, associative.
Laws
Algebraic laws.
- Is addition commutative and associative here? boundary
- What is the identity element? definition
Inverse
Subtraction.
Inverse
Inverses.
- Does every element have an additive inverse? boundary
- In which structure? definition
Computing Machine addition.
Precision
Floating point.
Precision
Precision.
- Could floating-point rounding affect the sum? boundary
- Is exact arithmetic needed? action
Overflow
Limits.
Overflow
Overflow.
- Could the sum overflow the data type? boundary
- How is it handled? action
Learning Teaching.
Strategies
Methods.
Strategies
Strategies.
- Which strategies help learners add? action
- How is carrying taught? action
Checking
Errors.
Checking
Checking sums.
- How can a sum be checked? action
- What errors are common? boundary
Classifiers Filled
- Family
- Thing Registry
- Category
- Cross-cutting context
- Entry kind
- thing
- Plane
- XCT
- Domain
- XCT.QTY
- Other names and narrower kinds
- vector addition, addition of complex numbers, matrix addition
What it is Filled
The basic arithmetic operation of combining quantities to give their sum, written a + b; it extends to vectors, matrices, complex numbers and other structures with defined addition.
Why it exists Filled
Let an agent handle addition by domain, properties and methods, from arithmetic to algebraic structures.
Distinguishing features Filled
- Binary operation giving a sum
- Commutative and associative for numbers
- Identity element zero
- Defined differently in different structures
What robots and AI may and may not do Filled
Must not
- Add quantities with different units without converting.
- Alter totals in financial or official records.
- Present copied answers as a student's own work in graded assessment.
Only with a human decision
- Correcting totals in financial or official records.
May
- Add numbers and other quantities correctly, stating units.
- Check sums in records it is authorized to audit.
Moral aspects Filled
- Wrong sums in bills, pay or votes can wrong many people.
Who is affected
- People relying on totals
- Students
Owners Filled
Steward
Nobody owns it; it belongs to mathematics, held in common.
Links to other meta-models Filled
parent
- Q164307 - registry parent class
related
- binary operation - category
- subtraction - operation
- multiplication - operation
- arithmetic and algebra - fields
What else AI and robots need to interact with it Filled
Identity and identifiers required Filled
- Vercy registry: vr.tr.addition
- Wikidata: Q32043 (https://www.wikidata.org/wiki/Q32043)
Direct properties not applicable Not applicable
Not applicable
Plane XCT: no invented physical properties.
Recognition optional Filled
- Plus sign
- Sums, totals and carries
- Vector addition by components
- The plus sign and sums.
Capabilities and actions required Filled
- add numbers
- add vectors and matrices
- teach addition strategies
- check sums and carries
Hazards and failure modes required Filled
- Floating-point rounding errors
- Adding quantities with different units
- Overflow in computing
Standards and interfaces required Filled
- ISO 80000-2 notation
Context of use required Filled
- Combining quantities in everyday life, science and computing.
- addition of natural numbers
- addition of integers and reals
- complex addition
- vector and matrix addition
- modular addition
Sources Filled
- Wikidata item Q32043: addition - identity and sense of the item
- Wikipedia: Addition - general description of the item
Open questions
- Should addition in structures be separate entries?
- How should teaching strategies be linked?
- How should floating-point issues be recorded?
Machine files
Provenance
thing registry research (pass 2) · unreviewed
Built from: models/things/publications/thing-q32043/spec.json