As a student, one of the most important things you can do to succeed in your academic career is to take effective notes. Handwritten notes are especially beneficial because they allow you to actively engage with the material and retain information better than typing on a computer. If you’re a student of Set Theory, we’ve got some great news for you – we have handwritten notes covering various topics in Set Theory that you can download for free in PDF format.
The topics covered in our notes include Set, Function, One-One function, Onto Function, Equivalent Sets, Countable Set, Properties of Sets, and more. These topics form the foundation of Set Theory, and understanding them is crucial for success in advanced mathematics and computer science.
One of the most important topics covered in our notes is Countable Set. In our notes, we show that the set of rational numbers, Q, is countable. This may come as a surprise to many students, as Q seems like an infinitely large set. However, our notes explain how we can create a one-to-one correspondence between the set of rational numbers and the set of natural numbers, proving that Q is indeed countable.
Another topic covered in our notes is Countably Infinite Set. We explain the concept of a countably infinite set, which is a set that has the same cardinality as the set of natural numbers. Our notes provide several examples of countably infinite sets, including the set of even numbers and the set of all integer multiples of 3.
Our notes also include a proof of the theorem “Every Infinite set has a countable subset.” This theorem is important because it tells us that even though infinite sets may seem overwhelmingly large, they can still be broken down into countably infinite subsets. Understanding this theorem is key to developing a strong intuition for infinite sets and their properties.
In addition to these topics, our notes cover other important concepts in Set Theory, such as Equivalence Classes, Cantor Theorem, Partial Ordering Relation, and Totally Ordered Set. Whether you’re a beginner in Set Theory or an advanced student looking to deepen your understanding of these topics, our notes are a valuable resource.
In conclusion, if you’re a student of Set Theory, our handwritten notes are an excellent resource to supplement your learning. They cover important topics in Set Theory, including Countable Set, Countably Infinite Set, and the proof of the theorem “Every Infinite set has a countable subset.” By downloading our notes in PDF format, you can study at your own pace and refer back to them whenever you need a refresher. Good luck with your studies!