 Taken together, these principles have been shown to have remarkable consequences for the indecomposability of subsets of the continuum. Not only is the intuitionistic continuum indecomposable (that is, cannot be partitioned into two nonempty disjoint parts), but, assuming the Continuity Principle and Kripke’s Scheme, it remains indecomposable even if one pricks it with a pin. The intuitionistic continuum has, as it were, a syrupy nature, so that one cannot simply take away one point. If in addition Bar Induction is assumed, then, still more surprisingly, indecomposability is maintained even when all the rational points are removed from the continuum.