Measurement, Approximation and Interval Arithmetic - Real Numbers and Limits Math Foundations

Explore measurement, approximation, and interval arithmetic in this 42-minute lecture from the MathFoundations series. Delve into the differences between arithmetic laws for natural numbers and integers, and briefly examine rational number intervals. Learn about multiplying intervals, analyze examples of interval arithmetic, and understand the sub-distributive law. Investigate the challenges associated with "real number" arithmetic and gain insights into the logical complexities of modern pure mathematics. Enhance your understanding of foundational mathematical concepts and their practical applications in this comprehensive exploration of interval arithmetic and its implications.

Intro to measurement and approximation
Multiplying intervals
An example of interval arithmetic
Laws of arithmetic for intervals with natural numbers
Arithmetic for intervals
Examples of interval multiplication
Laws of arithmetic for interval integers
Sub-Distributive law
Story with rational intervals
The serious problems with "real numbers"