Lesson 5

Some sets differ only in how their objects are named: for example, \(2^{[n]}\) and \(\{0,1\}^{n}\). An example for \(n=3\):

The same applies to orders: the inclusion order on \(2^{[n]}\) and the product order on \(\{0,1\}^{n}\) are, in a sense, the same, even though they are defined on different sets. We will formalize this below.