Well, Bernoulli umbra is an umbra whose moments are the Bernoulli numbers.

But what is it philosophically?

For instance, we can consider imaginary unit $i$ an umbra with moments $\{1,0,−1,0,1,\ldots\}$, hyperbolic unity $j$ as an umbra with moments $\{1,0,1,0,1,0,\dots\}$.

Can we in the same way somehow think about Bernoulli umbra as some kind of a hypercomplex "number", vector or series or whatever other object that can be geometrically represented and imagined, that has algebraic properties besides having those moments?

Is there any geometric or set-theoretic object that represents Bernoulli umbra?

11more comments