In part one of our two part examination of sequences and series, we look specifically at the finite variety.
We have reached the point where we can properly introduce infinite processes, and show that the set of rational numbers cannot include all of the numbers we’ll need. You can read this lesson here.
Now that the field axioms have been established, we can formally define the rational numbers. Most elementary school students refer to them as “fractions.” You can read this lesson here.
The second volume of Math From Scratch is here, with the intent to reach the definition of the real numbers. We will cover some Euclidean geometry along the way. This lesson covers the axioms of an algebraic field.
Equipped with the Minkowski diagrams of the previous lesson, we can now explore some logical implications that are frequently labelled paradoxes. This lesson reveals that these are not true paradoxes, but are instead complex and counterintuitive logical consequences of the theory. As usual, it is up to the reader to decide whether to continue with or without the math.