Small, yet Significant Infinities

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“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.”
― John Green, The Fault in Our Stars

Interpretation: Hazel knew to herself that everyone doesn’t, in reality, have infinite lives. Moreover, if you are terribly ill, to live or not to live tomorrow is truly already beyond our knowledge. We don’t have any choice. However, what Hazel did is that even for a short period of time, she felt loved and shared it with Augustus, and within that time-frame, she made everything to possibly last forever. Love, and the certainty of how we feel are the most important things in this world, and once we achieved both at last, we should be thankful, not only to our partners, but also to God.


2 thoughts on “Small, yet Significant Infinities

    • Practically speaking, we can assume that they do both (the intervals from 0 to 1 and from 0 to 2) have the same number of numbers since by sense, they are construed as still infinities. But I guess theoretically speaking (through using the set theory), the infinity of 0 to 1 and the infinity of 0 to 2 are different. Moreover, if we list all (which of course is tedious) subsets of the infinite set {0, 1} and all subsets of the infinite set {0, 2}they neither be equal (having the same subsets) nor equivalent (all subsets can be put into 1 to 1 correspondence) sets .


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