Given two numbers a, b transcendent and algebraically dependent and c one number, if a, b and c are algebraically dependent, then c is transcendent. Is this result true? If so, how can I prove it?
2026-03-29 15:54:49.1774799689
Given two numbers a, b transcendent and algebraically dependent and c one number, if a, b and c are algebraically dependent, then c is transcendent
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This is false. Indeed, take $(a,b,c)=(\pi,2\pi,0)$. Then $2a−b=c$, however $c$ is not transcendental.