## How Big is Infinity?

If you have read my article on Counting the Real Numbers, and enjoyed it, you should watch the incredible 7-minute TED video below, a more comprehensive explanation about that topic. It explains the cardinality of rational and irrational numbers and the continuum hypothesis.  A must view for mathematics students and enthusiasts.

## Are all infinities created equal?

A one-minute explanation that not all infinities are equal. The video shows that the number of real numbers from 0 to 1 is  greater than the number of all natural numbers 1, 2, 3, 4, and so on.

If the video is too fast or too short, you can read a more detailed explanation in  Counting the Real Numbers.

## Sets: Terminologies, Notations, and Operations

As a preparation for more posts on probability, statistics, permutations and combinations, we familiarized ourselves last week with the different terminologies and notations of probability.  We continue in this post by studying set terminologies, notations, and operations. Note that this is also the third post in the Set Primer Series; the first and second are Introduction to Sets and  Subset: a set contained in a set.

Universal Set

The universal set is the set that contains all the elements under discussion. If we talk about the letters  in the English alphabet, then the universal set contains all the 26 letters. In set theory, universal set is usually denoted by $U$.

In the following discussion, we let $U$ be the set of integers, $E$ be the set of even integers, and $O$ be the set of odd integers.  The following are the common operations on sets.

Intersection

If sets $A$ and $B$ have elements in common they form a set written as $A \cap B$. This is the intersection of $A$ and $B$.

Example: If we let $A = \{1, 2, 3, 4, 5\}$ and $B = \{2, 4, 6\}$ then $A \cap B = \{2,4\}$. » Read more