Definition:Subset/Notation

Notation for Subset

Notation in the literature for the concept of a subset can be confusing.

On $\mathsf{Pr} \infty \mathsf{fWiki}$, the convention is as follows:

$\subseteq$ is used for the general subset

$\subsetneq$ or $\subsetneqq$ is used for the concept of a proper subset.

The notation $\subset$ is deprecated on $\mathsf{Pr} \infty \mathsf{fWiki}$, on the grounds that it can mean either.

Sources

• 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 6$: Subsets
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): subset or subclass
• 1996: Winfried Just and Martin Weese: Discovering Modern Set Theory. I: The Basics ... (previous) ... (next): Basic Notations
• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $3$: The Natural Numbers: $\S 4$ A double induction principle and its applications
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): proper subset
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): proper subset