Which infinity is larger ?

This is a topic, or perhaps at least two topics.

https://en.wikipedia.org/wiki/Cardinality

https://en.wikipedia.org/wiki/Measure_(mathematics)

Cardinality generalizes the concept of counting, while measure generalizes the concepts of length, area, volume, etc. Talking about the real numbers, in terms of cardinality there are exactly as any real numbers between 1 and 2 as between 1 and 100. Looking at it using measure, specifically the usual measure for length, the interval from 1 to 2 has length 1 and from 1 to 100 has length 99, so the latter is larger.

The notion that there's the same "count" of numbers between 1 and 2 as between 1 and 100 might be unintuitive at first. Here's a classic on that:

https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel

/r/learnmath Thread