Describing the real numbers as a complete ordered field.

[@GNavarro97]

Great channel for beggining undergraduates mathematicians.

[@academyofuselessideas]

Thank you for your kind comment! I hope you enjoy the other videos we have... feel free to comment and let us know your thoughts and feedback!

[@MasterGxt]

It's a great channel for anyone with a love for mathematics

[@academyofuselessideas]

@@MasterGxtThank you!

[@pleaseenteraname1215]

Go Go gorlack

[@academyofuselessideas]

Gorlack is slowly taking control over Slim like in the movie Invasion of the body snatchers... but it is okay because Gorlack is actually cooler 🙃

[@pleaseenteraname1215]

@@academyofuselessideas I would have liked to say something about video but I stopped understanding at ablian groups. Great Video though slim.

[@academyofuselessideas]

thanks... you can ignore the Abelian group thing... Mathematicians are obnoxious sometimes (or to be more fair, I am obnoxious sometimes). To describe the real numbers (which is the purpose of this video), we need to define what a complete ordered field is. But this definition has a lot of moving pieces. So if one just list all the properties, one end up with a lot of information... Studies show that humans can only keep a very few number of concepts in their heads, so in order to tackle complex subjects they have to create compartments... If you have to remember that addition is associative, has identities, and has inverses, you are already using 3 different concepts... but if you create a compartment with those three concepts, you only use one concept... This is more or less how we build up concepts.... So, that's why I wanted to talk about Abelian groups here (so it is easier to remember the field axioms)... However, there is a simpler route... instead of remember all the field axioms, the easiest way is to replace the concept of "field" by the concept of "rational numbers"... If you keep that example in mind, all those axioms will make much more sense (The technique here is just to keep an example in mind... Richard Feynman used that technique when thinking about problems, and he claimed that keeping examples in mind was one of the reasons why he could solve problems quickly)... Hopefully that helps!

[@pleaseenteraname1215]

@@academyofuselessideas I will keep this in mind and I will see rest of series, The video title is compels me to understand the video, I love numbers!.

[@academyofuselessideas]

@@pleaseenteraname1215 And feel free to ask any questions that come to your mind!