This raises the possibility of reinstating the centrality of the ordinal numbers as the fundamental numbers even in the case of infinite sets, thus making ordinality the foundation of cardinality for all sets. In work after 1883, Cantor attempted to show that the alephs actually represent a scale of infinite cardinal number. For instance, it is shown that the ordinal numbers are comparable, i.e., for any two ordinal numbers α, β, either  α &lt; β, α = β or  α &gt; β, a desirable, perhaps essential, property of counting numbers. Through this, comparability therefore transfers to the alephs, and Cantor was able to give clear and appropriate arithmetical operations of addition, multiplication and exponentiation, generalising the corresponding notions for finite collections, and the statement and proof of general laws concerning these.