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Sunday, August 25, 2013

The Fault in Our Stars has some wrong math (spoilers)

"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."

I love that this character used mathematics to express her love to her dying boyfriend. It still bugs me that the math is wrong. Gus gave her the same size infinity between 0 and 1 as she would have gotten between 0 and 2, or 0 and a million. I'm afraid this makes me a heartless asshole.

(The author acknowledges that the math is wrong, and claims it was intentional. I believe him. I don't know what to do with it.)


  1. The math isn't exactly wrong. While the two sets have the same cardinality, [0,1] is a set of measure 1 and [0,2] of measure 2, so it is (in some sense) twice as big an infinite set.

  2. I agree with a few of my college math classes we talked about the sizes of different infinities...and something about adding a hotel room to a hotel with infinite rooms. I don't know - I had some strange professors :)

    I'm a new follower - thanks for all of your great posts!

  3. Dammit Kate! I'm reading this book right now. I'm like right in the middle of it when they're in Amsterdam. You gotta warn me about spoilers!

  4. Oops. Sorry. I thought I was the absolute last person in the world to read this. I'll change the post title.

  5. John Green like always has poured his heart in his work.This book makes you laugh,cry and makes us understand the world of people having cancer.The best virtue of this book is that it is not a slow book i.e it doesn't slow down.Some books after some amount of time get a bit boring but in case of this book it keeps getting interesting and there are many plots that are unexpected.I won't do any spoilers but I will like to tell you a bit about it.It is story about a girl named Hazel Grace who has Lung Cancer and how she is kinda alone and a boy named Augustus Waters comes into her life and her life revolves and changes because of him.

  6. Check out NCTM's Mathematics Teacher journal, September 2013 ... just came in the mail. There is an article, "Are All Infinities Created Equal?" Great discussion for students!

  7. I read this book earlier this year as part of a collaborative project, along with a group of teacher friends from all different subject areas. This project was spearheaded by two cutting edge and excellent ELA educators, Cheryl Morris and Andrew Thomasson. I loved the book! I didn't even notice the math at the end, but now that you mention it, I also love that Hazel mixes the language of love with the language of math. Coincidence? I think not!


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