| ▲ | knome 3 days ago | |
>There are more prime numbers than there are squares of integers. all integers have a square, while not all integers are prime. in any given span, you'll see more primes than squares, however. more dense? | ||
| ▲ | Someone a day ago | parent | next [-] | |
> all integers have a square, while not all integers are prime. That’s true, but I don’t see how that’s an argument. “All integers have a prime ‘the nth prime’, while not all integers are squares” similarly is true, but not an argument as to which set is denser. | ||
| ▲ | SamBam 3 days ago | parent | prev | next [-] | |
They must both have the same cardinality, ℵ0, because they are both infinite subsets of the natural numbers, and so can each be laid out in order and paired with every natural number. | ||
| ▲ | madcaptenor 3 days ago | parent | prev [-] | |
For example, the number of primes less than n is around n/log(n) while the number of squares less than n is around sqrt(n), which is much smaller. | ||