Second part on the construction of the real numbers. Here, we define the reals explicitly using what are called Dedekind Cuts. Then, we see how this definition results in the number system we know and love.

First part of a two-part post on the construction of the real numbers. This gives an introduction to the problem and outlines the issues with the rational numbers that motivate the construction of a better system.

It is essentially impossible to learn modern mathematics without being familiar with basic concepts from set theory. The reason is because definitions in math typically rely on sets and and the relationships between them.