Discrete topology on a two-point set is not Cardinality =1=\aleph_1

Automatically deduced from the following:
Cardinality =1=\aleph_1
Cardinality 3\geq 3
Cardinality $\geq 4$ ⇒ Cardinality $\geq 3$¬Finite ⇒ Cardinality $\geq 4$Finite ⇒ CountableCardinality $=\aleph_1$ ⇒ ¬CountableCountableFiniteCardinality $=\aleph_1$Cardinality $\geq 3$Cardinality $\geq 4$