O'Reilly logo

All the Mathematics You Missed by Lori Pedersen, Thomas A. Garrity

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

Chapter 10

Countability and the Axiom of Choice

Basic goal:

Comparing infinite sets

Both count ability and the axiom of choice grapple with the elusive notions behind “infinity”. While both the integers Z and the real numbers  R are infinite sets, we will see that the infinity of the reals is strictly larger than the infinity of the integers. We will then turn to the Axiom of Choice, which, while straightforward and not an axiom at all for finite sets, is deep and independent from the other axioms of mathematics when applied to infinite ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required