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Construction junctions are diamonds. They show where multiple structures must coexist on the same carrier and satisfy compatibility conditions.

Canonical static concept record

Integer fraction pairs

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Summary

Pairs $(a,b)\in\mathbb Z\times(\mathbb Z\setminus\{0\})$ representing fractions $a/b$ .

Record metadata

Canonical name: Integer fraction pairs
Concept ID: rational_fraction_pairs
Content version: 2.3.0
Primary field: Mathematics
Fields: Mathematics
Primary domain: Number theory
Domains: Number theory, Set theory, Algebra
Alternate terminology: No alternate terminology is currently authored for this record.
Concept type: Quotient presentation

Carrier(s)

set $\mathbb Z\times(\mathbb Z\setminus\{0\})$

Data

equivalence relation $(a,b)\sim(c,d)$ iff $ad=bc$

Canonically induces

field-of-fractions quotient

Concept sources

Wikipedia — Rational number — Rational number · encyclopedic reference · source ID wp-rational-number
nLab — rational number — rational number · mathematical reference · source ID nlab-rational-number

Incoming relations (arrows to this concept)

Each relation below ends at this concept.

Integers $\mathbb Z$ Integer fraction pairs

Permalink to relation

This is an authored directed relation from the source endpoint to the target endpoint.

Relation ID: integers_to_rational_pairs
Relation type: Canonical construction canonical-construction
Direction: source → target
Endpoint roles: source: Canonically constructs; target: Canonically constructed from
Authored annotation: form nonzero-denominator fractions

Authored explanation

Use integer numerator–denominator pairs with nonzero denominator before quotienting.

How to interpret this relation type

Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.

Relation sources

Wikipedia — Rational number — Rational number · encyclopedic reference · source ID wp-rational-number
nLab — rational number — rational number · mathematical reference · source ID nlab-rational-number

Outgoing relations (arrows from this concept)

Each relation below starts at this concept.