A Rigorous Procedure for Generating a Well-ordered Set of Reals without use of Axiom of Choice/Well-ordering Theorem

In Set theory, well-ordering of the Reals is a major difficulty. A well-ordering of the Reals is achievable under conventional Zermelo Fraenkel Set theory with the Axiom of Choice (ZFC). The Axiom of Choice (AC) had to be added to

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