Suppose you have a collection of pairs of shoes and pairs of matching socks. Let’s think about two questions: Can you create a set containing one shoe from each pair? The answer is yes, for example you could take the left shoe from each pair. Can you create a set containing one sock from each…
Tag: set theory
The pigeonhole principle
Let me tell you about one of my favorite things. The pigeon and dove family, Columbidae, is a group of widespread and common birds. Members of this family were domesticated thousands of years ago and they have had symbolic importance throughout history. Many species continue to live closely with humans. People who keep pigeons are…
Thinking about infinit(ies): The math tea argument
Are there undefinable numbers? Numbers that exist, but that we can’t identify or talk about? According to one argument, there must be such numbers, since there must be more numbers than definitions. Preliminaries First, some background about infinity. We’ll start by talking about the foundations of math using set theory. A set is an unordered…
thoughts on mind 