Factorial
In mathematics, the factorial of a non-negative integer , denoted by , is the product of all positive integers less than or equal to .
At a glance
Key signals
0% cross fields · reaches 0 more
- Mathematics
- Discrete Mathematics
- Combinatorics
- Explanation
- Examples
- Misconception
- Sourced relations
- 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
FactorialenablesPermutationEstablished
factorial enables permutation.
Mechanism: The number of ways to order n items is n factorial (n!), the building block of counting arrangements.
- Wikipedia (English & German editions) verifiedmoderate evidence
Permutationdepends onFactorialEstablished
Permutation depends on Factorial.
Mechanism: The number of permutations of n items is n factorial.
Structural role & consequence
Interpreted from the current atlas graph — what the connections mean, not just how many there are.
Directly enables 1 concept; following enables/causes relations, 1 concept is downstream across 3 disciplines.
structural · Follows only enables/causes dependency edges — not general relatedness.
Currently dark in the atlas: no key date stored · 2 of 2 of its relations lack claim-level evidence.
atlas representation · Describes the current Thinking OS representation, not the state of the world.
All 1 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
1 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, 1 in total, across 3 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 Permutation and Permutation.
Through this lens it connects to Permutation and Permutation.
Through this lens it connects to Permutation and Permutation.
Formula
Source: Wikidata
Related ideas to explore
Concepts that look related but are not yet connected here — candidates for a connection to reason about, not established links.
This idea also appears in…
The same structure shows up in other disciplines. These are real recurrences drawn from the graph — a starting point for asking “what carries over, and what changes?”
Compounding21 disciplines · 16 concepts
Concepts
shares a mental model
shares a mental model
shares a mental model
shares a mental model
shares a mental model
shares a mental model
Mental models at work here
- Connects 1 other ideas across 3 disciplines.
- Most of its connections are of the “Cause & effect” kind.
- It exercises 1 reusable thinking pattern.
Derived from the graph’s real structure — observations, not a score.
Sources
- Wikipedia (English & German editions) verifiedmoderate evidence
- Wikidata verifiedmoderate evidence
- Unitary Group Theory and the Discovery of the Factorial Schur Functions (2000) verified
- An umbral setting for cumulants and factorial moments (2006) verified
- Fractional factorial designs (1993) verified
- On intermediate factorial languages (2009) verified
- Factorial Theorem for Computing the Factorial of Positive Real Number (2023) verified