Reddit mentions of Beyond Infinity: An Expedition to the Outer Limits of Mathematics

Posting this reply for others, since you've decided to avoid learning anything today

I'd recommend Beyond Infinity, by mathematician Eugenia Cheng. It nicely explores this topic.

We are not talking about the hierarchy of infinities here, since both sets are countable infinities - as you pointed out.

But even countable infinities have scale. Picture 2 sets, defined as follows:

a = {n, 0 < n <= ∞}
b = {1000n, 0 < n <= ∞}

Simply, we have a - a set of all integers, and b - the same set with a multiplier attached

It is easy to see that for any given value of n, b will always yield a larger result.

So although if were to take the sums of a and b from n=0 to n=∞ we would find both sets to be infinite, set b is said to be a larger infinite set than a.

For an even lighter read but still good check out Eugenia Cheng's books... (and YouTube videos)...

Beyond Infinity (Set theory and Infinity)

https://www.amazon.com/Beyond-Infinity-Expedition-Limits-Mathematics/dp/0465094813/ref=sr_1_3?keywords=how+to+bake+pi&qid=1555533568&s=digital-text&sr=1-3-catcorr

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How to Bake π (category theory!)

https://www.amazon.com/How-Bake-Pi-Exploration-Mathematics-ebook/dp/B00TT1VLSG/ref=sr_1_1?keywords=how+to+bake+pi&qid=1555533464&s=digital-text&sr=1-1-catcorr

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The Art of Logic in an Illogical World

https://www.amazon.com/Art-Logic-Illogical-World-ebook/dp/B0791N8R3V/ref=sr_1_2?keywords=how+to+bake+pi&qid=1555533568&s=digital-text&sr=1-2-catcorr