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Universe of One

A dictionary of complete sets

About this dictionary

This is a working surface for cataloging complete sets: minimal, lawful collections that close a structure without redundancy.

Each entry names a set, states its boundary conditions, and explains how it becomes “complete” in its own universe.

Entries

Orthogonal Basis in ℝ³

Domain: Linear Algebra

Cardinality
3 vectors
Completeness condition
Spans ℝ³ and all vectors are mutually orthogonal.

A set of three nonzero, mutually orthogonal vectors forms a complete basis for ℝ³. No proper subset spans the space; any additional vector is redundant with respect to the span.

minimal basis geometry

Major Triad

Domain: Music Theory

Cardinality
3 pitch classes
Completeness condition
Root, major third, and perfect fifth present.

The major triad is the minimal set of pitch classes that establishes a major tonality. Removing any tone breaks the functional identity; adding tones (extensions, doublings) does not change the core set.

tonal center minimal

HTTP Request Line

Domain: Web Protocols

Cardinality
3 tokens
Completeness condition
Method, Request-URI, and HTTP version present.

The request line is the minimal complete set that defines the intent of an HTTP request. Without any one of the three tokens, the message cannot be interpreted according to the protocol.

protocol interface

How entries are structured

  1. Name: A concise label for the complete set.
  2. Domain: The universe in which the set is defined (math, music, protocol, garment, market…).
  3. Cardinality: How many elements are in the set.
  4. Completeness condition: The rule that makes this set “enough and no more.”
  5. Explanation: Plain-language description of why this set is minimal and complete.
  6. Tags: Chips for quick scanning and cross-linking.