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.
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.
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.
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 .
In the following discussion, we let be the set of integers, be the set of even integers, and be the set of odd integers. The following are the common operations on sets.
If sets and have elements in common they form a set written as . This is the intersection of and .
Example: If we let and then . » Read more