  We explore when the silting-discreteness is inherited. As a result, one
obtains that taking idempotent truncations and homological epimorphisms of
algebras transmit the silting-discreteness. We also study classification of
silting-discrete simply-connected tensor algebras and silting-indiscrete
selfinjective Nakayama algebras. This paper contains two appendices; one states
that every derived-discrete algebra is silting-discrete, and the other is about
triangulated categories whose silting objects are tilting.
