You should be able to solve this.

True or false: Are algebraic numbers countable?
You can't use axiom of choice.

>>13 Here


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Within each degree of polynomial we can inject into the natural numbers as there are only a countable number of each degree (A finite union is still countable without AC), so we assosciate to each polynomial a second number, it's order in this ordering."

Might need choice here, but I can explicity construct an injection so it's fine.