{ 17, $$\pi$$, New York City, King Willem-Alexander, Euromast }
is the set that contains the entities 17, $$\pi$$, New York City, King Willem-Alexander, and Euromast. These entities are the elements of the set. Since we assume that a set is completely defined by the elements that it contains, the set is well-defined. Of course, we still haven’t said what it means to be an ‘entity’. Something as definite as ‘New York City’ should qualify, except that it doesn’t seem like New York City really belongs in the world of mathematics. The problem is that mathematics is supposed to be its own self-contained world, but it is supposed to model the real world. When we use mathematics to model the real world, we admit entities such as New York City and even Euromast. But when we are doing mathematics per se, we’ll generally stick to obviously mathematical entities such as the integer 17 or the real number $$\pi$$. We will also use letters such as a and b to refer to entities. For example, when I say something like “Let A be the set{a, b, c}”, I mean a, b, and c to be particular, but unspecified, entities.