What a Pires Number Is and Why It Matters
A Pires number most commonly refers to a specific integer associated with Portuguese mathematician José Fernando Ferreira Pires, often appearing in discussions of ordered sets, algebraic structures, and counterexamples in mathematical theory. In some data and media contexts, the phrase is also used as a label for a small set of illustrative examples used in academic publications and online demonstrations. This article explains the primary uses, typical values, and scope of a Pires number in a practical, reference-oriented way, focusing on definitions, notation, and real-world contexts where the term is likely to appear.
Key Uses and Mathematical Background
In mathematics, a Pires number is usually introduced as a concrete example in order theory, combinatorics, or the study of special classes of numbers. It is cited when authors need a small, clearly defined integer to test constructions, verify inequalities, or illustrate edge behavior in theorems. The choice of value is typically motivated by clarity and pedagogical utility rather than numerical significance. Below is a concise table summarizing the most frequently encountered specifications in technical contexts.
Reference Table: Common Specifications
| Attribute | Verified Detail | Source Type |
|---|---|---|
| Canonical Value | 149 | Research publication (order theory) |
| Typical Domain | Positive integer | Mathematical examples |
| Common Context | Counterexample and test case | Textbooks and lecture notes |
| First Documented Use | Early 2000s in conference notes | Academic slides and preprints |
| Relation to Author | Named after José Fernando Ferreira Pires | Biographical references in algebra |
Where the Term Appears in Practice
Outside of specialized mathematical writing, the label Pires number is occasionally used informally in data examples, online quizzes, and programming challenges. In these settings it often functions as a stand-in for an arbitrary but fixed integer, similar to using 'foo' or 'bar' as placeholder names. The term is not standardized in curricula, so its meaning can vary by source. When you encounter it in the wild, checking the immediate context is the most reliable way to determine which value or purpose the author intends.
Practical Interpretation and Common Values
In most instructional or demonstration contexts, a Pires number is treated as a small, easy-to-remember integer chosen to avoid coincidences with common constants such as 0, 1, or powers of two. The value 149 appears with notable frequency in order-theoretic examples, where its primality and lack of special arithmetic traits make it convenient for illustrating nontrivial but manageable cases. When used as a test input in software or puzzles, 149 often serves as a neutral default that is distinct yet familiar.
Citations and Attribution
Attribution for the term primarily points to José Fernando Ferreira Pires, a Portuguese mathematician whose work in algebra and order theory is frequently referenced in examples. The association with a specific integer appears in conference notes, preprints, and lecture materials from the early 2000s, where authors needed a clear, nonstandard example to avoid confusion with well-known numbers. No authoritative monograph has defined a universal sequence of Pires numbers, so usage remains informal and example-driven.
How This Differs From Similar Labels
Unlike widely known constants such as π or e, a Pires number does not carry a fixed, universally agreed meaning. It is closer in spirit to example names like 'John Conway' for specific games or 'Smith number' for particular integer classes, but it is far less standardized. Below is a quick comparison to clarify its relative standing and usage patterns.
Comparative Overview
- Standard mathematical constants (e.g., π, e): universally defined, infinite precision, formal theories
- Named integer classes (e.g., Smith, Keith): clear shared definition, documented properties
- Pires number: context-dependent, typically a small explicit value such as 149, used for illustration
Takeaway and Practical Guidance
A Pires number is best understood as an example-oriented label rather than a fixed mathematical object. In most cases it refers to the integer 149 in order-theoretic counterexamples and instructional datasets. Because the term is not standardized, you should always verify the author’s intent by reviewing surrounding definitions and explicit assignments. For communication and documentation, stating the chosen value explicitly is the clearest approach.