How to Write Proofs in Set Theory with the Math Sorcerer

Introduction to Proof Writing with Set Theory

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How to Write Proofs in Set Theory with the Math Sorcerer

What You Will Learn!

How to Write Mathematical Proofs with Sets
The Mathematical Notation Surrounding Sets
The Definition of a Set and Subset
The Definition of Union, Intersection, Relative Complement(Set Minus), and Absolute Complement
How to Show one Set is a Subset of Another
How to Show Two Sets are Equal
How to Use Various Proof Techniques in Set Theory Proofs
How to use the Method of Double Inclusion
How to Prove Sets are Equal without the Method of Double Inclusion
How to Do a Proof by Contradiction
Understand the Common Sets found in Mathematics including the Natural Numbers, Integers, Rational Numbers, Real Numbers, and Complex Numbers
Understand what Empty Set actually is
Understand Venn Diagrams
Understand the Powerset and How to Find it
Understand Cardinality(Bonus Section, More Advanced)
How to Prove Two Sets have the Same Cardinality(Bonus Section, More Advanced)

Description

This is a course on PROOF WRITING with Sets:)

This course starts with some VERY BASIC definitions regarding the theory of sets. Some simple examples are given at the beginning, but soon after, the PROOFS begin!!

Important Note: A formal prerequisite for this material is an understanding of mathematical logic. However I have tried to explain the ideas from logic as they come up in the proofs.

The best way to learn to write proofs is to watch someone else give careful proofs and then try to do it on your own.

This is the MANTRA behind this course which is full of beautiful 100% correct well written proofs!!!

Basically just,

1) Watch the introduction videos if you need to. These cover the very basic things that you should know regarding sets.

2) Watch the PROOF videos in ANY order. Take notes, try to understand them.

3) Try to do the proofs on your own! If you can't, watch the video and cheat and try again.

It takes A LOT of effort to learn to write proofs like the ones you see in these videos, so don't feel discouraged if you find it difficult, it is supposed to be tough.

This is an EXCELLENT course for anyone who wants to jump into proof writing. I hope you enjoy watching these videos and working through these problems as much as I have:)

Note this course has lots of very short videos. If you are trying to learn math then this format can be good because you don't have to spend tons of time on the course every day. Even if you can only spend time doing 1 video a day, that is honestly better than not doing any mathematics. You can learn a lot and because there are so many videos you could do 1 video a day for a very long time. Remember that math can be challenging and time consuming, so if you just do a little bit every day it can make your journey much more enjoyable. I hope you enjoy this course and learn lots of mathematics.