It should be noted that both aperture
and focal length are intrinsic properties of a lens, having nothing to do with the size of the sensor behind it. Manufacturers have no problem printing the FF-equivalent focal length in big numbers on fixed-lens cameras, sometimes along with the aperture like Panasonic does with “25-600” and “F2.8” on the FZ300 (though Leica puts the real focal length on the lens itself).
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It’s not true that ‘light gathering is the same’. Light gathering is a function of the size of the iris diaphragm, not the f/number. The lens on the Ricoh GR IV gathers the amount of light of an 18.3mm f/2.8 lens, not a 28mm f/2.8 lens. The latter would have a larger iris diaphragm and gather more total light.
Exposure is a function of the light intensity (per unit area), and that is proportional to f/number. Also, even though the exposure triangle doesn’t change, image noise at the same ISO setting is higher with a smaller sensor. There’s no free lunch.