Let
X
X
be a smooth projective variety. The Iitaka dimension of a divisor
D
D
is an important invariant, but it does not only depend on the numerical class of
D
D
. However, there are several definitions of “numerical Iitaka dimension”, depending only on the numerical class. In this note, we show that there exists a pseuodoeffective
R
\mathbb {R}
-divisor for which these invariants take different values. The key is the construction of an example of a pseudoeffective
R
\mathbb {R}
-divisor
D
+
D_+
for which
h
0
(
X
,
⌊
m
D
+
⌋
+
A
)
h^0(X,\left \lfloor {m D_+}\right \rfloor +A)
is bounded above and below by multiples of
m
3
/
2
m^{3/2}
for any sufficiently ample
A
A
.