 The classical Continuum Hypothesis states that there is no set whose cardinality lies strictly between that of the set \(\bN\) and that of \(\textrm{sb}(\bN)\). We can state this more formally as follows:  \[ \forall C(\bN ≲ C≲ \textrm{sb}(\bN) \Rightarrow C \cong \bN \vee C \cong \textrm{sb}(\bN)) \]  or, equivalently,  \[ \forall C(\bN ≲ C≲ \textrm{sb}(\bN) \wedge \neg(C ≲  \bN) \Rightarrow C \cong \textrm{sb}(\bN)) \]  Constructively acceptable classical equivalents of these two statements are:  \[ \forall C(\bN ≲ C ≲ \textrm{dch}(\bN) \Rightarrow C \cong \bN \vee C \cong \textrm{dch}(\bN)) \]  and the one that we take as our constructive Continuum Hypothesis, \(\textrm{CH}\),  \[ \forall C(\bN ≲ C≲ \textrm{dch}(\bN) \wedge \neg(C \cong \bN) \Rightarrow C \cong \textrm{dch}(\bN)) \]