Set
In mathematics, a set is a collection of different things; the things are called elements or members of the set and are typically mathematical objects: numbers, symbols, points in space, lines, other geometric shapes, variables, functions, or even other sets.
At a glance
Key signals
0% cross fields · reaches 4 more
- Mathematics
- Discrete Mathematics
- Set Theory
- Explanation
- Examples
- Misconception
- Sourced relations 2
- Attribution
Dependencies
What this concept builds on and what it makes possible — derived from the atlas’s dependency, causal and structural relations, not from every related edge.
Enables · leads to
Cartesian Productis derived fromSetEstablished
Cartesian Product is derived from Set.
Functiondepends onSetEstablished
function depends on set.
Mechanism: A function depends on sets: it is a rule assigning to each element of one set (the input) exactly one element of another (the output).
- Wikipedia (English & German editions) verifiedmoderate evidence
System context
Setis part ofVector spaceEstablished
set is part of vector space.
Mechanism: A vector space is a set of vectors with rules for adding them and scaling them, forming the arena of linear algebra.
- Wikidata verifiedmoderate evidence
Elementis part ofSetEstablished
Element is a part of Set.
Subsetis part ofSetEstablished
A subset is contained in a set.
Mechanism: Every element of the subset is also an element of the larger set.
Subsetis aSetEstablished
Subset is a kind of Set.
Structural role & consequence
Interpreted from the current atlas graph — what the connections mean, not just how many there are.
Currently dark in the atlas: no key date stored · 13 of 13 of its relations lack claim-level evidence.
atlas representation · Describes the current Thinking OS representation, not the state of the world.
Structural neighbourhood: 12 → 30 → 51 concepts reachable within 3 hops.
structural · Structural reach — being reachable is not the same as being understood.
All 12 of its relationships stay within its own discipline — a field-specific concept in the current atlas.
structural · Structural graph analysis — not a claim of importance, causation or history.
cross-field
12 within-field, 0 cross-field
Strengths & constraints
Constraints
- Evidence coverage currently thin in the atlas — few of its relationships carry claim-level evidence. atlas representation
- No dated history stored — the atlas records no key date for this concept. atlas representation
Conditions
- Read structurally — most of its relationships carry no external evidence yet, so claims here are graph-derived. structural
Dependency radial
What this concept builds on (left) and what it makes possible (right) — derived from dependency and causal relations.
What builds on this
1 concept build on this directly, 2 in total, across 4 disciplines.
Structural downstream reach along dependency edges — not a claim of historical necessity.
Seen through each discipline
How this concept sits in each of its fields — derived from its real connections in the graph, not asserted.
Through this lens it connects to Function, Subset, Cardinality and Set theory.
Through this lens it connects to Function, Subset, Cardinality and Subset.
Related ideas to explore
Concepts that look related but are not yet connected here — candidates for a connection to reason about, not established links.
- Connects 12 other ideas across 3 disciplines.
- A cross-disciplinary bridge — its connections reach into 4 other fields.
- Most of its connections are of the “Teaching link” kind.
Derived from the graph’s real structure — observations, not a score.
Sources
- Wikipedia (English & German editions) verifiedmoderate evidence
- Wikidata verifiedmoderate evidence