The cardinal numbers are well - ordered by indexing with the ordinal numbers ( see Cardinal number , formal definition ) .
This also establishes that there is no greatest ordinal number ; conversely , the latter statement implies Cantor 's paradox .
Since the cardinal numbers are well - ordered by indexing with the ordinal numbers ( see Cardinal number , formal definition ) , this also establishes that there is no greatest ordinal number ; conversely , the latter statement implies Cantor 's paradox .