few more tweaks to intro to halo mass function
@@ -314,7 +314,7 @@ where the angular lensing convergence power spectrum $C^{ab}_\ell$ is given abov
\cont{Mass function definitions. Discussion of precision of Tinker mass function fits.}
-The calculation of the halo mass function focuses around the spherical overdensity method of halo finding, in which the size of a halo can be defined with:
+Being able to calculate the halo abundance as a function of mass is a necessary step to being able to constrain cosmology with probes such as galaxy clustering. While analytic functions are the traditional means of predicting evolution, calibration is frequently required against cosmological simulations. In order to reach the high precision for cosmological constraints in a self-consistent fashion, it is ultimately necessary to use cosmological simulations; we implement this with halo mass functions with parameters fit to these simulations. The calculation of the halo mass function focuses around the spherical overdensity method of halo finding, in which the size of a halo can be defined with:
\begin{equation}
\bar{\rho}(r_{\Delta}) = \Delta \times \bar{\rho_{\mathrm{m}}},
