In various mathematical forums, mostly those of a logical flavor, I regularly see people asking basic questions about constructive mathematics. I also see misconceptions about constructive mathematics. I shall make a series of posts, *Constructive Gems and Stone*s, which will answer basic questions about constructive mathematics, and will hopefully help fix wrong ideas about constructive mathematics.

A constructive *gem* is something nice about constructive mathematics that makes you want to know more about it. In contrast, a constructive *stone* is a complication in constructive mathematics which does not exist in the classical counterpart.

Here we go! The first one is about finite sets.