Number Theory: Notation Reference explains divisibility, congruences, primes, gcd, modular inverses, and proof notation.
Core notation for Number Theory
In number theory, the notation usually represents finite sets, graphs, integers, indices, recurrences, coefficients, and counting conventions. The table below gives a compact starting set for number theory; define any local variation before the first calculation.
| Concept | Notation | How to read it |
|---|---|---|
| Binomial coefficient | \binom{n}{k}=\frac{n!}{k!(n-k)!} | number of k-subsets of an n-set |
| Sequence | (a_n)_{n\ge0} | indexed family of terms |
| Recurrence | a_n=a_{n-1}+a_{n-2} | term defined from earlier terms |
| Graph | G=(V,E) | vertices and edges |
How to read a complete expression
Read \binom{n}{k}=\frac{n!}{k!(n-k)!} as “number of k-subsets of an n-set.” Identify the outer operation first, then its inputs, index set, conditions, and result type. This prevents a superscript, bar, vertical line, or styled letter in number theory from being interpreted by appearance alone.
Conventions that belong in the notation table
- State whether indexing begins at zero or one.
- Distinguish ordered from unordered selections.
- Declare whether graphs are directed, simple, weighted, or allow loops.
Cross-checks before reuse
- Enumerate a small case.
- Verify boundary indices.
- Compare a recurrence with its initial conditions.
Accessibility and portability
Keep the number theory source selectable and editable. For an isolated character in number theory, Unicode text may be sufficient; for structured expressions, preserve LaTeX, MathML, or a native equation object. When an image of number theory is unavoidable, describe the operation, inputs, conditions, and conclusion rather than listing glyph names.
Verification checklist
- Enumerate a small case.
- Verify boundary indices.
- Compare a recurrence with its initial conditions.
- Confirm every symbol used in number theory has one defined meaning in the local context.
- Reopen the exported file for Number Theory: Notation Reference and compare it with the editable source.
How this guide was checked
Page purpose: number theory notation reference — Look up notation, definitions, and usage conventions
Automated quality check: Kept noindex until critical findings are resolved.
Verification references
These primary standards and official documentation pages were used to check character identity, syntax, or platform behavior described above.
- The Unicode StandardUnicode Consortium — Character identity, encoding, names, and conformance.
- Unicode Technical Report #25: Unicode Support for MathematicsUnicode Consortium — Mathematical character usage, variants, and notation support.
- LaTeX Project DocumentationThe LaTeX Project — LaTeX syntax, authoring model, and official documentation links.
- MathML CoreW3C — Semantic web mathematics elements and browser behavior.