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There was another Hebrew word then in use for the whole Old Testament as well as "ketuvim".
Seder Eliyahu Rabbah says on this, "Keitzad yitkaymu shnei ketuvim halalu?"
These three, then, the Law = Torah (the "Te" of the Tenakh), the Prophets = Neviim (the "Na" of the teNAkh), and the Writings = ketuvim (the "K" of the tenaKH), compose the three parts bearing various weights of the Old Testaments of Jesus 'day.