# algebraic numbers

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• Jul 28th 2011, 04:53 AM
thomasboateng
algebraic numbers
x is algebraic and let y = x + 3. Is y algebraic? and why is it?
• Jul 28th 2011, 05:06 AM
alexmahone
Re: algebraic numbers
Quote:

Originally Posted by thomasboateng
x is algebraic and let y = x + 3. Is y algebraic? and why is it?

Let f(x) be the irreducible polynomial for x over F. Then, the irreducible polynomial for y over F is f(y-3). So, y is algebraic.
• Jul 28th 2011, 12:00 PM
FernandoRevilla
Re: algebraic numbers
More general, $\mathbb{A}=\{x\in\mathbb{R}:\; x\mbox{ & algebraic & over}\;\mathbb{Q}\}$ is a field (non finite extension of $\mathbb{Q}$)