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.

# education

## Math From Scratch 25: Infinite Processes

November 1, 2012 by W. Blaine Dowler education, math, math from scratch Bureau 42 Teaches

## Math From Scratch 24: Defining the Rational Numbers

October 1, 2012 by W. Blaine Dowler education, math, math from scratch Bureau 42 Teaches

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.

## Math From Scratch 23: The Field Axioms

September 1, 2012 by W. Blaine Dowler education, math, math from scratch Bureau 42 Teaches

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.

## Summer School 2012.9: Cosmology

August 31, 2012 by W. Blaine Dowler education, physics, relativity, summer school Bureau 42 Teaches, Summer School

## Summer School 2012.8: Black Holes and Worm Holes

August 24, 2012 by W. Blaine Dowler education, physics, relativity, summer school Bureau 42 Teaches, Summer School

## Summer School 2012.7: Gravity

August 17, 2012 by W. Blaine Dowler education, physics, relativity, summer school Bureau 42 Teaches, Summer School

## Summer School 2012.6: Electricity and Magnetism

August 10, 2012 by W. Blaine Dowler education, physics, relativity, summer school Bureau 42 Teaches, Summer School

## Summer School 2012.5: Energy and Momentum

August 3, 2012 by W. Blaine Dowler education, physics, relativity, summer school Bureau 42 Teaches, Summer School

## Summer School 2012.4: Fun with Paradoxes

July 27, 2012 by W. Blaine Dowler education, physics, relativity, summer school Bureau 42 Teaches, Summer School

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.

## Math From Scratch 26 – Sequences and Series

December 1, 2012 by W. Blaine Dowler education, math, math from scratch Bureau 42 Teaches

In part one of our two part examination of sequences and series, we look specifically at the finite variety.