Definition:Symmetric Difference/Notation

Notation for Symmetric Difference

There is no standard symbol for symmetric difference. The one used here, and in general on $\mathsf{Pr} \infty \mathsf{fWiki}$:

$S \symdif T$

is the one used in 1996: Winfried Just and Martin Weese: Discovering Modern Set Theory. I: The Basics.

The following are often found for $S \symdif T$:

$S * T$

$S \oplus T$

$S + T$

$S \mathop \triangle T$

According to 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics: symmetric difference:

$S \mathop \Theta T$

$S \mathop \triangledown T$

are also variants for denoting this concept.

2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.): symmetric difference recognizes a further variant:

$S \mathop \nabla T$

Sources

• 1964: Steven A. Gaal: Point Set Topology ... (previous) ... (next): Introduction to Set Theory: $1$. Elementary Operations on Sets
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): symmetric difference
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): symmetric difference
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): symmetric difference