Is it possible to create a telescope with only one convex lens?

Specifically, is the image I drew below possible?  

(This was supposed to be rotated 90 degrees counterclockwise.)

![Picture of my hypothesis(?)](https://i.stack.imgur.com/KUkVl.jpg)

In this picture, the object (smaller thing) is supposed to be infinitely far away. The lens focuses the light rays on to the eye (top in picture). Then the eyes "sees" as if it is enlarged to be the bigger image (bigger thing).

Some of my friends argue that humans can only see light rays which are parallel to each other. My counter argument is the picture below:

![Picture of eye seeing at infinity and nearer than infinity.](https://i.stack.imgur.com/DfteP.png)

So if anybody could explain to me why or why not could I create a telescope out of a single convex lens. Thank you!