whether the thought had been previously adumbrated, perhaps confusedly, i know not, but the name of Bertrand Russell has become associated with the assertion that:
the number $2$ is the set of all sets which contain exactly two elements.
i think there is even today some adherence to this rather neat definition.
but my elementary knowledge of these matters suffices to give rise to two questions:
a) should not Russell have said: the proper class of sets having exactly two elements?
b) does this imply that to understand the meaning of the symbol $2$ it is necessary to have a model of the entire class of transfinite cardinals, and to accept something like the Axiom of Choice? and is the theory of these infinities in fact research into the Kolmogorov Complexity of the concept of a finite cardinal?