The extension field $K(\alpha)$ of a base field $K$ , where $\alpha$ is a transcendental element with respect to $K$ , is a simple transcendental extension of $K$ . All such extension fields are isomorphic to the field $K(X)$ of rational functions in one indeterminate $X$ over $K$ , and thus to each other.

Example. The subfields $\mathbb{Q}(\pi)$ and $\mathbb{Q}(e)$ of $\mathbb{R}$ , where $\pi$ is Ludolph's constant and $e$ Napier's constant, are isomorphic.