Name: mod01lec09 - Infinite Sets and Axiom of Choice | 影片 | 乾淨世界
Uploaded: 2023-12-02T17:43:04.207Z
Duration: 19 min 15 s
Description: We describe a fundamental axiom in set theory, called the Axiom of Choice. It is an "axiom" (i.e. an agreed upon rule) because it cannot be proved using the bas... | 影片 | 乾淨世界

NPTEL-NOC IITM

https://video5-us-west.cloudokyo.cloud/video/v6/1a/3f/e4/1a3fe496-ffbd-4c03-a461-ec917fb73a4f/master.m3u8

We describe a fundamental axiom in set theory, called the Axiom of Choice. It is an "axiom" (i.e. an agreed upon rule) because it cannot be proved using the basic rules of set theory. This was the main reason that it was not universally accepted for some time in the past. However, modern mathematicians agree that it is useful and use it without hesitation. We use the axiom of choice to give a theorem characterizing infinite sets, in particular we show that a set is infinite if and only if it has a bijection with a proper subset of itself.