A black hole has an infinitesimally small volume, which means that its density (mass/volume) becomes massive, almost infinite. That doesn’t mean that the mass is infinite.
If a black hold had “infinite” mass, it would pull everything into it. The Newton’s law of gravitation states that the gravitational force is proportional to the masses of each body; if one mass was “infinite,” then the other body would be experiencing “infinite” attraction.
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