How to Set Up Fractions IV - The Relation Between Fractions and Other Number Systems

Explore the relationship between fractions and other number systems in this 30-minute lecture. Gain insights into the positioning of rational numbers within the broader context of number systems, including natural numbers, integers, and complex numbers. Challenge conventional understanding of "real numbers" in pure mathematics and examine the ancient Greek distinction between counting and measuring. Discover how this leads to different types of number systems, from natural numbers used in counting to more geometrical numbers like line segments used in measuring. Ideal for high school teachers and undergraduates seeking to deepen their understanding of fundamental mathematical concepts and challenge prevailing notions about numbers.

Introduction
Proportions
Discrete vs Continuous
Unit Segments
Interpretation of Fractions
Bridging the gap