However, in constructive mathematics, the two notions of subsingleton are no longer the same, because the axiom of excluded middle no longer holds true. Instead, one usually defines a subsingleton as the first definition, and the second definition is then referred to as about decidable subsingletons.

Every subsingleton $S$ comes with an injection$i \colon S \to 1$ into a singleton$1$, and is thus is a (structural) subset of $1$. A subsingleton is also decidable in the subset sense: defining the relation $x \in_1 S$ as

$x \in_1 S \coloneqq \exists y \in 1.i(x) = y$

for all elements $x \in 1$, $x \in_1 S$ or $\neg (x \in_1 S)$.