Three things: First, this research didn't show that all infinities are equal, it just showed that two particular ones are equal. Indeed, in Cantor's formulatio

Three things: First, this research didn't show that all infinities are equal, it just showed that two particular ones are equal. Indeed, in Cantor's formulation, the powerset of any set is larger than the original set, which immediately shows that there is no largest infinite set. Second, this research wasn't about ℵ₀ and c at all, but about another pair. Third, the issue about ℵ₀ and c isn't about whether they're equal, but whether there is or isn't a third infinity that's larger than ℵ₀ and smaller than c. It's already known that both answers (yes and no) are consistent with standard mathematical axioms. Edit: this result does have some connection with the continuum hypothesis, but I don't know exactly what that connection is. However, these researchers definitely didn't claim either to prove or disprove the continuum hypothesis.