Order Isomorphism/Examples/Real Arctangent Function
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Example of Order Isomorphism
The real arctangent function $\arctan$ is an order isomorphism between the set of real numbers $\R$ and the open real interval $\openint {-\dfrac \pi 2} {\dfrac \pi 2}$ under the usual ordering.
Proof
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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