Explanation: Initial-final mass function (IFMF) of non-rotating primordial stars (Z = 0). The x-axis gives the initial stellar mass. The y-axis gives both the final mass of the collapsed remnant (thick black curve) and the mass of the star when the event begins that produces that remnant (e.g., mass loss in AGB stars, supernova explosion for those stars that make a neutron star, etc.; thick gray curve). We distinguish four regimes of initial mass: low mass stars below ~10 M_sun that from white dwarfs; massive stars between ~10 M_sun and ~100 M_sun; very massive stars between ~100 M_sun and ~1000 M_sun; and supermassive stars (arbitrarily) above ~1000 M_sun. Since no mass loss is expected for Z = 0 stars before the final stage, the grey curve corresponds approximately to the line of no mass loss (dotted), except for ~100-140 M_sun where the pulsational pair-instability ejects the outer layers of the star before it collapses, and above ~500 M_sun where pulsational instabilities in red supergiants may lead to significant mass loss. Since the magnitude of the latter is uncertain, lines are dashed. In the low mass regime we assume, even in Z = 0 stars, that mass loss on the asymptotic giant branch (AGB) removes the envelope of the star leaving a CO or NeO white dwarf (though the mechanism and thus the resulting initial-final mass function may differ from solar composition stars). Massive stars are defined by stars that ignite carbon and oxygen burning non-degenerately and do not leave white dwarfs. The hydrogen-rich envelope and parts of the helium core (dash-double-dotted curve) are ejected in a supernova explosion. Below initial masses of ~25 M_sun neutron stars are formed. Above that, black holes form, either in a delayed manner by fall back of the ejecta, or directly during iron core collapse (above ~40 M_sun). The defining characteristic of very massive stars is the electron-positron pair instability after carbon burning. This begins as a pulsational instability for helium cores of ~40 M_sun (M_ZAMS = ~100 M_sun; ZAMS = "zero-age main sequence"). As the mass increases, the pulsations become more violent, ejecting any remaining hydrogen envelope and an increasing fraction of the helium core itself. An iron core can still form in hydrostatic equilibrium in such stars, but it collapses to a black hole. Above a helium core mass, M_He, of ~63 M_sun or about M_ZAMS = 140 M_sun, and on up to M_He = 133 M_sun or about M_ZAMS = 260 M_sun) a single pulse disrupts the star. Above 260 M_sun, the pair instability in non-rotating stars results in complete collapse to a black hole.