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as it did in his case and has done in most
cases where the logician has attempted to advance
his science. The common sense idea of
being greater than is that if one collection
contains a member representative of every member
of another collection and more beside,
it is greater than that other; and consequently
an infinite collection is greater
than itself. But Bolzano's definition
does not allow any collection to be
greater than itself, if there are two
collections the As and the Bs and if
there is any possible relation, r, in which
every A stands to a B to which no other
A is r, then, says Bolzano, we will
say that the collection of As is not
greater than that of the Bs. If there be
no possible relation of that sort the
collection of As is greater than that of the
Bs. But, thereupon, there at once