Infinities don’t care about the actual numbers in the set, but about the cardinality (size). Obviously the numbers between 0,1 and 1,2 are different but have the same size.
But 0,1 and 0,2? Size is unintuitive for infinities because they are … infinite. So the trick is to look for the simplest mathematical formula that can produce a matching from every number of one set to every number in the second. And as somebody has said, every number in 0,2 can be achieves by multiplying a number in 0,1 by 2. So there is a 1 to 1 relation between 0,1 and 0,2. Ergo they are the same size.
Infinities don’t care about the actual numbers in the set, but about the cardinality (size). Obviously the numbers between 0,1 and 1,2 are different but have the same size.
But 0,1 and 0,2? Size is unintuitive for infinities because they are … infinite. So the trick is to look for the simplest mathematical formula that can produce a matching from every number of one set to every number in the second. And as somebody has said, every number in 0,2 can be achieves by multiplying a number in 0,1 by 2. So there is a 1 to 1 relation between 0,1 and 0,2. Ergo they are the same size.