Axiom of Choice

Axiom of Choice.
unobjectionable logical principle.
Ernst Friedrich Ferdinand Zermelo.
1871-1953.

Ernst Zermelo was a mathematician who is best known for his work in set theory and for formulating the Axiom of Choice. He also made significant contributions to the theory of games and was awarded the Cantor Medal in 1931 for his contributions to mathematics.

The Axiom of Choice is a mathematical principle that confidently states that given any collection of non-empty sets, there exists a function that can choose one element from each set in the collection. This is the explanation you will see throughout the internet or in books.

If you watched other videos before this, you are probably asking. Why does no one explain this the way everyone understands? Fortunately, there is a way to make it straightforward. However, know that it is not an accepted axiom by many mathematicians.

Imagine you have a finite or infinite amount of each species in containers that start from where you are and stretch to infinity and none of the containers are empty. You randomly choose one from each container and put it in a new container which would hold a well-ordered infinite amount of each kind to associate its member species.

Zermelo proposed the Axiom of Choice in 1904. It became an important tool in many areas of mathematics, particularly in set theory, topology, and functional analysis. It is controversial but, the Axiom of Choice is widely accepted by mathematicians as a legitimate principle.