It is named for Hans Christian Andersen's famous story of The Ugly Duckling, because it shows so as to, all things life form equal, an ugly duckling is just as similar to a swan as two swans are to each other. It was future plus proved by Satoshi Watanabe in 1969. We have no preconceived ideas or biases about what sorts of categories are "natural" or "usual" and what are not.

So we have to consider all the possible classes so as to could be, every one the possible habits of creation sets out of the n objects. Whoops. We can't. If you have trouble seeing that, pick two elements plus reorder the bits so they are the first two, and picture the numbers sorted lexicographically. And is the same as the figure of those content by one.