= Two abundance crossings of the Press-Schechter mass function
{title2=$\mathcal N_{\ln M}\propto\nu e^{-\nu^2/2}$}
At fixed mass, the <Press-Schechter halo mass function> has abundance per logarithmic interval proportional to $\nu e^{-\nu^2/2}$. This increases as $\nu$ falls from infinity to one and then decreases as $\nu$ falls toward zero, reflecting incorporation of small <dark-matter haloes> into larger ones. A target below the maximum therefore has two mathematical crossings if the <linear growth factor> can increase without limit. The large-$\nu$ crossing describes first appearance; the small-$\nu$ crossing is late depletion. Late vacuum domination limits growth, so a formal future crossing need not be reached physically.
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