  We show three basic properties on the image Milnor number $\mu_I(f)$ of a
germ $f\colon(\mathbb{C}^{n},S)\rightarrow(\mathbb{C}^{n+1},0)$ with isolated
instability. First, we show the conservation of the image Milnor number, from
which one can deduce the upper semi-continuity and the topological invariance
for families. Second, we prove the weak Mond's conjecture, which says that
$\mu_I(f)=0$ if and only if $f$ is stable. Finally, we show a conjecture by
Houston that any family
$f_t\colon(\mathbb{C}^{n},S)\rightarrow(\mathbb{C}^{n+1},0)$ with $\mu_I(f_t)$
constant is excellent in Gaffney's sense. By technical reasons, in the two last
properties we consider only the corank 1 case.
