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You can make sense of a percentage of natural numbers with the concept of natural density: https://en.wikipedia.org/wiki/Natural_density https://en.wikipedia.or
by ja3k 7y ago
You can make sense of a percentage of natural numbers with the concept of natural density: https://en.wikipedia.org/wiki/Natural_density https://en.wikipedia.org/wiki/Natural_density
The natural density of a set is the limit as N goes to infinity of the proportion of the numbers up to N which are in the set.
For instance the natural density of primes, squares and cubes is 0 and the natural density of even numbers is 1/2. But all these sets are infinite so the same cardinality.
- throwawaymath 7y agoThank you, but your last sentence is not really correct. The concept of cardinality captures different sizes of infinity. This is why I mentioned countable and uncountable infinites upfront: a countably infinite set and an uncountably infinite set do not have the same cardinality, but both are infinite.