Lesson 1A: Types of Sets & Set Notation

How big is infinity? Is infinity a number? Is anything bigger than infinity? How far away is from here to infinity ?

Toward the end of the 19th century, German mathematician Georg Cantor searched for answers to these types of questions.

To talk about infinity, he first had to find a way to define it mathematically. That was not easy! Although the concept was known for centuries, infinity was just a vast concept considered by many not worth studying or understanding.

In fact, many mathematicians of the day considered infinity to be distasteful—something for philosophers to discuss. It was an idea that at the time was scorned.

In this climate, Georg Cantor published the first proof of the existence of infinity. His achievement was made remarkable by his use of an ancient branch of mathematics known as set theory . This was something like building a spaceship out of a wheelbarrow! At first, Cantor's ideas were not well received; they were too innovative. Eventually, Cantor's ideas prevailed and became part of mainstream mathematics. For his contributions, he is identified by many as the father of set theory.

No one can expel us from the paradise Cantor has created.
David Hilbert, 20th century mathematician

Set theory is among the most powerful tools of modern mathematics, yet the basic idea was used as far back as Aristotle—things can be grouped into sets.

The set is the mathematical object that Cantor scrutinized and which this Training Camp will introduce to you.

By the end of this lesson, you should be able to

provide examples of empty sets, disjoint sets, subsets, and universal sets in context, and explain your reasoning
determine the elements in the complement of two sets
organize and interpret information using graphic organizers such as Venn diagrams