Real Arctangent Function is Order Embedding into Reals

Theorem

The real arctangent function $\arctan: \R \to \R$ is an order embedding on the set of real numbers under the usual ordering.

Proof

This theorem requires a proof. In particular: straightforward but tedious. We should have Real Arctangent Function is Increasing for a start but we don't yet. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Sources

• 1996: Winfried Just and Martin Weese: Discovering Modern Set Theory. I: The Basics ... (previous) ... (next): Part $1$: Not Entirely Naive Set Theory: Chapter $2$: Partial Order Relations