Extended Rational Numbers in Practice - Real Numbers and Limits

Explore the concept of extended rational numbers in this 39-minute mathematics lecture. Delve into the extension of rational numbers to include expressions with zero denominators, and discover their practical applications in various mathematical fields. Learn how extended rationals can be used to visualize graphs of rational polynumbers, potentially leading to new insights in calculus. Examine the connection between extended rationals and projective geometry, particularly in the context of the one-dimensional projective line. Investigate the parametrization of circles and conics using extended rationals, and consider the geometric interpretation of arithmetic operations on circular points. Gain a deeper understanding of this mathematical concept through examples in economics, graphing, and geometry.

Intro to extending our number system
Defining an extended rational number
Operations
Recover rational numbers
Extended rational number and economics
Graphing rational polynumbers
Projective geometry
Projective coordinates on a circle
Graphing