addition
Let an agent handle addition by domain, properties and methods, from arithmetic to algebraic structures.
Research draft, second pass
A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.
written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify
Researched by: Claude
Purpose and description
Let an agent handle addition by domain, properties and methods, from arithmetic to algebraic structures.
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.
What it is for: Combining quantities in everyday life, science and computing.
It can be add numbers; add vectors and matrices; teach addition strategies; check sums and carries.
Distinguishing features
Binary operation giving a sum
Commutative and associative for numbers
Identity element zero
Defined differently in different structures
What it looks like
The plus sign and sums.
How it is recognised
Plus sign
Sums, totals and carries
Vector addition by components
Related models
is a kind of - category
has inverse - operation
is repeated in - operation
is studied in - fields
In practice
Families and kinds
addition of natural numbers
addition of integers and reals
complex addition
vector and matrix addition
modular addition
Standards and regulation
ISO 80000-2 notation
Failure modes and hazards
Floating-point rounding errors
Adding quantities with different units
Overflow in computing
Also called
Where this came from
wikidata · CC0 1.0
Also registered as vr.tr.addition-location
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.
Domain What is added.
Domain decides rules.
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.
Properties enable reasoning.
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.
Computers add with limits.
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.
Addition is foundational.
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
What the second pass must settle
- Should addition in structures be separate entries?
- How should teaching strategies be linked?
- How should floating-point issues be recorded?