The proof of the equality of cardinal number between algebraic number set and natural number set Don't prove that the set of rational numbers is countable there Let's not just say that algebraic numbers are countable because equations are countable

The proof of the equality of cardinal number between algebraic number set and natural number set Don't prove that the set of rational numbers is countable there Let's not just say that algebraic numbers are countable because equations are countable

It should be known that the set of rational numbers is countable. Algebraic numbers are the roots of polynomials with rational coefficients. For a polynomial with rational coefficients of degree n, there are only a limited number of roots. All polynomials with rational coefficients of degree n have the same potential as Q ^ n, so they are countable