My Mom was always taking bits of plants and sticking them in water to see if they'd root. She rarely got around to potting them up, however, and I seem to have inherited both habits. One of the things that she had stuck in a styrofoam cup was a few pieces of (thornless) cactus. The cup eventually started to crumble, so I set it on top of a pot of dirt. That was a while ago. (Hint: my Mom died in 1989.)
The cactus seems to be perfectly happy, however, and blooms each spring. This year, it had four blooms on it, three at the same time. The cactus plant is a straggly thing, with some bits an inch or so wide, but thin, and limp... tendrils?... about as big around as a pencil. The flowers are the size of my fist.
The flowers face the East window, so to get pics of the lower blossoms, I had to open the window, then go outside.