A measurement of the double-differential inclusive jet cross section as a function of jet transverse momentum pT and absolute jet rapidity | y| is presented. The analysis is based on proton-proton collisions collected by the CMS experiment at the LHC at a centre-of-mass energy of 13 TeV. The data samples correspond to integrated luminosities of 71 and 44 pb(-1) for | y| < 3 and 3.2 < | y| < 4.7, respectively. Jets are reconstructed with the anti-k(t) clustering algorithm for two jet sizes, R, of 0.7 and 0.4, in a phase space region covering jet pT up to 2 TeV and jet rapidity up to | y| = 4.7. Predictions of perturbative quantum chromodynamics at next-to-leading order precision, complemented with electroweak and nonperturbative corrections, are used to compute the absolute scale and the shape of the inclusive jet cross section. The cross section difference in R, when going to a smaller jet size of 0.4, is best described by Monte Carlo event generators with next-to-leading order predictions matched to parton showering, hadronisation, and multiparton interactions. In the phase space accessible with the new data, this measurement provides a first indication that jet physics is as well understood at root s = 13 TeV as at smaller centreof-mass energies.