The history of natural numbers is probably as old as human civilizations, and we should feel comfortable with natural numbers without any explanations. But the transition from natural numbers to integers (the inclusion of zero and the negative counterparts of natural numbers) took a long time. The missing concept was the concept of zero, 0, which only arrived in Europe at about 1200 AD just in time for the Renaissance. We give a brief history of zero in Sect. 2.2. With the introduction of zero, the transition to introduction of negative numbers and rational numbers occurs relatively quickly as explained in Sect. 2.3. In Sect. 2.4, we revisit the importance of zero again. Because of zero, rational numbers can be represented by decimals, and this decimal representation of numbers led George Cantor to prove that there are “more” real numbers than natural numbers. This made people realize the need for a better understanding of what a real number is. We define real numbers using the completeness axiom in Sect. 2.5. We use the completeness axiom to prove the existence of \(\sqrt{2}\) in this chapter.