Why do some infinities seem bigger than others, and how do mathematicians compare their sizes?
In: Mathematics
One infinity being “larger” than the other is a mathematical concept. The formal name for the size of a set is called its cardinality. For finite sets, the cardinality is equal to the number of elements in the set. However for infinite sets, this definition is no longer useful. The basic infinity is the countable infinity (of size aleph-zero, another formal term). The simplest example is the cardinality of all natural numbers. The next larger infinity is the uncountable infinity an example is the cardinality of the set of all real numbers which would be aleph-one.
These concepts are not intuitive. So one would need a bit of learning about set theory to understand how and why these definitions “make sense”.
Larger infinities are also possible in mathematics like aleph-two etc etc but they become increasingly hard to describe and conceptualize and have no “real world” easy examples.
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