The second context in which an argument was given was an attempt by Cantor (in correspondence first with Hilbert and then Dedekind) to show that every set must have an aleph-number as a cardinal.[17] What Cantor attempts to show, in effect, is the following. Assume that Ω represents the sequence of all ordinal numbers, and assume (for a reductio argument) that V is a ‘multiplicity’ which is not equivalent to any aleph. Then Cantor argues that Ω can be ‘projected’ into V, in turn showing that V must be what he calls an ‘inconsistent multiplicity’, i.e., not a legitimate set. It will follow that all sets have alephs as cardinals, since they will always be ‘exhausted’ by such a projection by some ordinal or other, in which case they will be cardinally equivalent to some ordinal number-class.[18] Zermelo's dismissal of this attempted proof is no surprise, given the comments just quoted. But he also comments further here exactly on this ‘projection’: