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A singleton has the property that every function from it to any arbitrary set is injective. The only non-singleton set with this property is the [[empty set]].
 
The [[Bell number]] integer sequence counts the number of [[partitions of a set]] ({{OEIS2C|[https://oeis.org/A000110}} OEIS A000110]), if singletons are excluded then the numbers are smaller ({{OEIS2C|[https://oeis.org/A000296 OEIS A000296}}]).
 
== In category theory ==