But adopting the aleph scale as a framework for infinite cardinality depends on significant assumptions. It is clear that any collection in well-ordered form (given that it is represented by an ordinal) must have an aleph-number representing its size, so clearly the aleph-sequence represents the sizes (or powers as Cantor called them) of all the well-ordered sets. However, can any set be put into well-ordered form? A particular question of this form concerns the continuum itself: if the continuum is equivalent to the second number-class, then clearly it can be well-ordered, and indeed this is a necessary condition for showing that the continuum is represented at all in the scale. But can it be well-ordered? More generally, to assume that any cardinality is represented in the scale of aleph numbers is to assume in particular that any set can be well-ordered. And to assume that the aleph-sequence is the scale of infinite cardinal number is to assume at the very least that sets generally can be compared cardinally; i.e., that for any M, N, either M ≼ N or  N ≼ M, COMP for short. But is this correct?