Theorem on friends and strangers: If we have 6 people in a room, then 3 of them know each other or 3 of them don't know each other. Or should it say that at least 3 people don't know anyone or at least 3 people are friends? Then my teacher said we can extend this to infinite sets, saying there is an infinite amount of people that don't know each other or there is an infinite amount of people that know each other. But it seems like I could have both with infinite sets. We could have all the even number people be friends with their squares, And all the odd numbered people be friends with their squares and we will make sure that the even and odd number people are friends. This is not homework.