which is still undesignated. Now let this last thing just spoken of in $A$ get the number $n$ for its designation, then the number of things in $A = n$.

Moreover, Bolzano speaks about *quantities*. This too is one of Bolzano’s complicated terms. (Simons 2004). Here we will stick to Bolzano’s definition as given in *Paradoxes of the Infinite*. A *quantity, \[Grosse\]*, belongs to a kind of thing of which every two can have no other relation to one another than either being equal to one another, or one of them presenting itself as a sum that includes a part equal to the other one (§6). We see that pluralities are also quantities.

*An infinite quantity* is greater than every finite number of the unit taken. An *infinitely small quantity* is so small that every finite multiple of it is smaller than the unit. (§10). [^9]

A quantity $A$ is *infinitely greater* than $B$, if $A$ is infinitely greater than every finite number of $B$; we will denote that here as $A >> B$.[^10]

Bolzano defended the existence of actual infinity decades before Cantor. Cantor underpinned his belief in the existence of infinite cardinal and ordinal numbers with theology. (Dauben 