# Real Arctangent Function is Order Embedding into Reals

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## 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