Some, but not all, one-to-one correspondences can be written concisely as functions. Not every function between two sets is a one-to-one correspondence though! We still have to check that it sends exactly one element to exactly one element, and doesn't miss any.

**In the case of \(\mathbb{R}\) and \((0,1)\), there is a nice function that we can use, and it is in fact a one-to-one correspondence.** In the In-Depth explanation we'll go into more detail about why this function is a one-to-one correspondence between the set \((0,1)\) and \(\mathbb{R}\). **In this section we’ll just tell you what the function is and show you a picture.**