Einstein-de Sitter cumulative number counts ($N(<z_f)=\frac{8n_0{c}^3}{3H_0^3}[1-(1+z_f{)}^{-1/2}{]}^3$)

For constant comoving number density and complete selection in a spatially flat Einstein-de Sitter universe, integrate the present-epoch shell volume up to the population's formation redshift. The radial distance is $D_M=2c[1-(1+z{)}^{-1/2}]/H_0$, so the count per unit solid angle is $n_0{D}_M^3(z_f)/3$. It tends to a finite value as $z_f$ tends to infinity because this model's present comoving particle-horizon radius is $2c/H_0$. Formation, mergers or an incomplete observed sample change this ideal count.