Question

Suppose we are given a line segment of length 1. We say that a real number x is constructible if we can construct, with unmarked straightedge and compass, a line segment of length (So for example, -3 is constructible since we can construct a line segment of length 3 by joining three segments of length 1 along the same line.) Prove that the set G of constructible numbers is a field. (Constructible numbers are real numbers, so you don't need to prove all the boring properties like the distributive law - these can be taken for granted. Focus on proving that this set satisfies the closure properties.)

Answer 1

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