Definition:Halmos Symbol/Also defined as

Halmos Symbol: Also defined as

Some sources show the Halmos symbol, in some contexts, as a heavy vertical line:

$\Rule{3px} {2ex} {0ex}$ or $\Rule{5px} {2ex} {0ex}$

rather than a square, but the intention is the same.

This form is used, for example, by Donald E. Knuth in his The Art of Computer Programming to indicate the point of termination of an algorithm.

Some sources use $\Box$ in preference to $\blacksquare$.

However, $\mathsf{Pr} \infty \mathsf{fWiki}$ prefers to reserve $\Box$ for the end of a subproof within a long proof, as a way of breaking up the flow of thought for clarity.

Technical Note

In order to render $\blacksquare$, use the template {{qed}}.

In order to render $\Box$, use the template {{qed|lemma}}.

When {{qed}} is used, it automatically adds the page on which it is implemented to Category:Proven Results.

Sources

• 1955: John L. Kelley: General Topology ... (previous) ... (next): Preface
• 1964: William K. Smith: Limits and Continuity ... (next): Preface
• 1968: A.N. Kolmogorov and S.V. Fomin: Introductory Real Analysis ... (previous) ... (next): $\S 1.3$: Functions and mappings. Images and preimages: Theorem $1$ (footnote)
• 1977: Gary Chartrand: Introductory Graph Theory ... (next): Preface
• 1990: H.A. Priestley: Introduction to Complex Analysis (revised ed.) ... (previous) ... (next): Notation and terminology
• 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.1$: Algorithms
• 2021: Jay Cummings: Proofs ... (previous) ... (next): Chapter $1$: $1.1$ Chessboard Problems