Set Theory and Infinity

15 Jun 2015

Personal

To start off, I owe you an explanation why I didn’t have a post last week, and why this post deviates from our usual discussion.

Many people say that data science is the intersection of programming, statistics, and domain expertise. For me, I want that domain to be education – I’ve always had a passion for it. There’s a lot in the U.S. education system that could be improved upon, and I think the techniques of data science can help improve it.

So, when I stumbled upon the Khan Academy Talent Search, I knew I had to make a submission. The contest allowed me to stretch my educational muscles again by creating two 10 minute videos on anything subject I wanted.

Immediately, I thought back to a mathematical proof by Georg Cantor that showed that infinities could have different magnitudes. It was one of several mathematical revelations I was introduced to in high school that really got me excited about math in a way that I hadn’t gotten from my high school classes.

So, instead of a full blog post this week, I’m just going to link to the two videos I created that lead up to this amazing argument by Cantor, his diagonal argument. The first video is a general introduction to set theory, and gives you everything you need for the second video, which lays out the idea that infinite sets can have different sizes.

  1. Set Theory Basics
  2. Infinite Sets

In data science, we wouldn’t get very far without sets of data, and while grinding away on practical problems is fun and extemely useful, a good perspective of the theoretical will only enrich your understanding.

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