Definition:Binary Operation/Also known as
Binary Operation: Also known as
Some authors use the term (binary) composition or law of composition for (binary) operation.
Some sources refer to a binary operation just as an operation.
Most authors use $\circ$ for composition of relations (which, if you think about it, is itself an operation) as well as for a general operation.
To avoid confusion, some authors use $\bullet$ for composition of relations to avoid ambiguity.
1965: Seth Warner: Modern Algebra uses $\bigtriangleup$ and $\bigtriangledown$ for the general binary operation, which has the advantage that they are unlikely to be confused with anything else in this context.
1975: T.S. Blyth: Set Theory and Abstract Algebra uses $\intercal$, and calls it truc, French for trick or technique:
- The symbol $\intercal$ is called truc ("trook") and is French for "thingummyjig"! The idea it conveys is that what we call our law of composition does not matter, for what we are really interested in are sets of objects and mappings between them.
The $\LaTeX$ code for \(\intercal\) is \intercal .
Sources
- 1951: Nathan Jacobson: Lectures in Abstract Algebra: Volume $\text { I }$: Basic Concepts ... (previous) ... (next): Introduction $\S 2$: Product sets, mappings
- 1964: Iain T. Adamson: Introduction to Field Theory ... (previous) ... (next): Chapter $\text {I}$: Elementary Definitions: $\S 1$. Rings and Fields
- 1964: Walter Ledermann: Introduction to the Theory of Finite Groups (5th ed.) ... (next): Chapter $\text {I}$: The Group Concept: $\S 1$: Introduction
- 1964: William K. Smith: Limits and Continuity ... (previous) ... (next): $\S 2.1$: Sets
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text I$: Algebraic Structures: $\S 2$: Compositions
- 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $1$: Integral Domains: $\S 2$. Operations
- 1973: C.R.J. Clapham: Introduction to Mathematical Analysis ... (previous) ... (next): Chapter $1$: Axioms for the Real Numbers: $2$. Fields
- 1975: T.S. Blyth: Set Theory and Abstract Algebra ... (next): $\S 11$