Introduction

Before we can study set theory, we must take a step back and examine the foundations of mathematics.

When attempting to learn math from the beginning, there is always the question of where to start. Many books about set theory assume knowledge of logic, or sometimes include a minimal section on logic. If one tries to learn logic first to have a better understanding, they often find the logic books start off with a short section on set theory! So where do we begin? There are numerous different approaches, here we develop in the following order;

• Philosophy
• Metalanguage/Metatheories
  
• First-order logic
• ZFC Set Theory

From ZFC, most all of mathematics can be developed! We will begin our look at the foundations by examining philosophy.