- biunique correspondence
- bijective correspondence
are sometimes seen for bijection.
Authors who prefer to limit the jargon of mathematics tend to use the term one-one and onto mapping for bijection.
The symbol $f: S \leftrightarrow T$ is sometimes seen to denote that $f$ is a bijection from $S$ to $T$.
Also seen sometimes is the notation $f: S \cong T$ or $S \stackrel f \cong T$ but this is cumbersome and the symbol has already got several uses.
The $\LaTeX$ code for \(f: S \leftrightarrow T\) is
f: S \leftrightarrow T .
The $\LaTeX$ code for \(f: S \cong T\) is
f: S \cong T .
The $\LaTeX$ code for \(S \stackrel f \cong T\) is
S \stackrel f \cong T .
- 1951: Nathan Jacobson: Lectures in Abstract Algebra: I. Basic Concepts ... (previous) ... (next): Introduction $\S 2$: Product sets, mappings
- 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 3.3$. Injective, surjective, bijective; inverse mappings
- 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $1$: Mappings: $\S 13$
- 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 22$: Injections; bijections; inverse of a bijection
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics: Entry: bijection
- 2008: David Joyner: Adventures in Group Theory (2nd ed.) ... (previous) ... (next): Chapter $2$: 'And you do addition?': $\S 2.1$: Functions: Definition $2.1.6$
- 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $1$: General Background: $\S 1$ What is infinity?