What We Learn from the Cardinality of Infinity?

I took a math proof class last semester and we spend a huge chunk of time talking about cardinality, especially the cardinality of infinity, which is a rather new topic in the discussion of cardinality. Even though the proof is a lack of excitement for me, the idea of comparing uncountable and infinity is very beautiful and philosophical. But I didn’t think further.

Infinity is mysterious yet beautiful and that’s probably why people seem to like the infinity symbol very much for the representation of love. People always want more.

So I watched a very moving love story today called “The Fault in Our Stars”. It is about the love between two dying people. The play writing is amazing and the screen shoot is also very good. But what I found enlighten is a very short quote from an interesting book writer: “Some infinities are bigger than other infinities.”

My first reaction upon this line is go back to the math and confirms it is true. Then I realized how philosophical this problem can be. In the movie, the girl always wanted more days with the boy, always, eternally, forever. This are all infinity. Because we wanted infinity. But is there a smaller infinity?

Let’s switch unit from day to seconds, a day in seconds, in milliseconds can also be infinity. Maybe if we can switch the way we look at infinity, looking for a smaller set of infinity, we can realized how valuable are life, our work and our relationship can be.

Just like the story in the movie, the boy wanted to be loved by everybody, but then realized that love from a simple individual can also be infinity.

I tag this title with Math is because I like Math, but more importantly, I think there are always some good points behind the dry statement from a science book.

Lastly I hope you can appreciate this eulogy the girl wrote for the boy:

“There are infinite numbers between 0 and 1. There’s .1 and .12 and .112 and an infinite collection of others. Of course, there is a bigger infinite set of numbers between 0 and 2, or between 0 and a million. Some infinities are bigger than other infinities. A writer we used to like taught us that. There are days, many of them, when I resent the size of my unbounded set. I want more numbers than I’m likely to get, and God, I want more numbers for Augustus Waters than he got. But, Gus, my love, I cannot tell you how thankful I am for our little infinity. I wouldn’t trade it for the world. You gave me a forever within the numbered days, and I’m grateful.”

Originally published at www.wesleyq.me.