Bernays' phrase comparing sets/infinite to a piano extending in both directions

Question

I'm looking for a phrase that Bernays said about infinity. I remember it as "Infinity is like a piano extending in both directions without end", but I can't find it anywhere!

The most similar thing I found was:

"Also in the grounding of analysis that starts by considering number sequences, the number series is conceived of as a closed, surveyable system, akin to an infinite piano keyboard."

Any help would be greatly appreciated. If I'm using the tags incorrectly please let me know.

Answer 1

I think that it is a free translation of a sentence that we can find into :

• David Hilbert & Paul Bernays, Grundlagen der Mathematik, Vol I (1934), page 17.

The German text starting with : "Ähnlich verhält ..." (second paragraph) is translated as follows :

It is much the same in every case in which a person thinks he can show directly that some infinity is given in experience or intuition, for example the infinity of the tone series extending from octave to octave up to infinity, or the continuous infinite manifold involved in the passage from one color quality to another. Closer consideration shows in every case that in fact no infinity is given at all; rather it is interpolated or extrapolated through some mental process.