We show that everyK-finite decidable objectXof an elementary toposEis Dedekind-finite, i.e., that every monic endomorphism ofXis an automorphism. As an easy corollary, every epic endomorphism ofXis likewise an automorphism. The proof depends in part on an analysis of the finite cardinals ofEand in part on the equivalence, in any Boolean tbpos, ofKfiniteness and Tarski-finiteness (Theorem 6). HereXis Tarski-finite iff every inhabited collection of arbitrary elements of ωX(subobjects ofX) contains a ¨—minimal element.