  Donald Knuth introduced in The Art of Computer Programming (Vol 4a) a fast
approximation to the addition of integers (given in binary) in terms of
bit-wise operations by $a + b \; \approx \; a \oplus b \oplus ((a\land b) \ll
1).$ Generalizing this to infinite bit-strings we get a binary operation on
${\mathcal P}(\mathbb{N})$, the power-set of $\mathbb{N}$ (which we identify
with the collection of infinite bit-strings). We show that this operation is
``group-like'' in that it has a neutral element, inverses, but it is not
associative. There are a lot of questions left, which the author has not been
able to answer.
