= Age of a closed dust universe
{title2=$H_0t_0=\frac{\Omega_0(u_0-\sin u_0)}{2(\Omega_0-1)^{3/2}}$}
For an expanding <pressureless matter> universe with positive curvature, zero <cosmological constant> and present <scale factor> one, set $u_0=\arccos(2/\Omega_0-1)\in(0,\pi)$. The <closed matter-dominated Friedmann solution> then gives the displayed <age of an FLRW universe>. Its flat limit is $2/(3H_0)$, despite the individually vanishing numerator and denominator. To see this, write $\delta=\Omega_0-1$; then $u_0=2\arctan\sqrt\delta$ and $u_0-\sin u_0=(4/3)\delta^{3/2}+O(\delta^{5/2})$.
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