A student or graduate of Cambridge University, or a resident of Cambridge.
From Latin 'Cantabrigia' (Cambridge University's Latin name), plus '-ian' suffix, literally meaning 'one from Cambridge,' a term used especially in British academic contexts.
Cambridge's Latin name 'Cantabrigia' comes from the River Cam plus the Old English 'bridge,' so Cantabrigians literally come from the 'Cam-bridge'—yet the university abbreviates it to 'Cantab,' showing how even ancient academic titles get shortened by busy students.
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