VI. Proving the List L is Complete
The question remains as to whether or not the list L will contain all real numbers in [r1, r2]. We will prove that: All the real numbers in [r1, r2] are contained in the list L.
Proof by Construction/Contradiction: Create a number X such that r1 < X < r2 and assume that X ∉ L. Demonstrate that ‘r1 < X < r2 and that X ∉ L’ leads to a contradiction.
To create X we employ Cantor’s diagonal method: