@Vladimir Just as you can imagine that a hotel has an infinite number of rooms, you can imagine that an infinite number of guests live in it.
Both sets would have the cardinality of the natural numbers IN,
ℵ₀ (aleph 0 /aleph-naught). Georg Cantor, the creator of set theory, dealt with it.
But he lived after Goethe.
The differential and integral calculus were developed before Goethe independently by Leibnitz and Newton. But I do not know whether Goethe already knew the mathematical term infinity (∞).
But Goethe does not seem to have studied mathematics:Habe nun, ach! Philosophie,
Juristerei und Medizin,
Und leider auch Theologie!
Durchaus studiert mit heißem Bemühn.
Da steh ich nun, ich armer Tor!
Und bin so klug als wie zuvor;
I, Vers355 ff.Alas, I have studied philosophy,
the law as well medicine,
and to my sorrow, theology;
studied them well with ardent zeal,
yet here I am, a wretched fool,
no wiser than I was before.
Copyright © for the artistic translation: Peter Salm
PS: Would @Bookie
had lived in the Hilbert space, we both would have met there.