(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A real number x[tex]\in[/tex]R is called algebraic if there exists integers [tex]a_{0}[/tex][tex]x^{n}[/tex]+[tex]a_{n1}[/tex][tex]x^{n1}[/tex]+.....+[tex]a_{1}[/tex]x+[tex]a_{0}[/tex]=0.

Show that [tex]\sqrt{2}[/tex],[tex]\sqrt[3]{2}[/tex], and 3+[tex]\sqrt{2}[/tex] are algebraic.

Fix n[tex]\in[/tex]N and let [tex]A_{n}[/tex] be the algebraic numbers obtained as roots of polynomials with integer coefficients that have degree n. Using the fact that every polynomial has a finite number of roots, show that [tex]A_{n}[/tex] is countable.

2. Relevant equations

3. The attempt at a solution

Completely confused on this one.

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# Real number is Algebraic

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