User:Abcxyz/Sandbox/Dedekind Completions of Ordered Sets

Feel free to comment. --abcxyz (talk) 16:44, 9 January 2013 (UTC)

Uniqueness of Dedekind Completion
Let $Z$ be a Dedekind complete ordered set.

Let $h: S \to Z$, $\alpha, \beta: Z \to X$ be increasing mappings such that:
 * $\alpha \circ h = \beta \circ h = f$

Then $\alpha = \beta$.