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We call a collection of the members of which
the Syllogism of Transposed Quantity necessarily
holds an enumerable collection and one of
which this is not true or where there is a Fermatian relation
a denumeral collection,— in German abzählbar,
of one, it follows that it is true of every
enumerable collection.

All the whole numbers, properly so called, that is,
all numbers of which our system of so called Arabic notation
affords a definite symbol,— all the numbers
up to any one form an enumerable collection.
But the entire collection of whole
numbers capable of representation in that
system is a collection not enumerable,
but innumerable. And the single multitude
of all the whole numbers, or of any such endless
series of which all the members up to any member form an enumerable
collection is called the denumeral collection,
“abzählbar” in German. The denumeral multitude
is a single multitude of the class of innumerable multitudes.