Is an infinitely small percentage equal to zero percent?

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Just came across a tweet with the following

0% of all integers are prime.

Thinking about that sentence as real numbers (0% of all reals are prime), in order to calculate that percentage, one ends up dividing by $\infty$ (even though smaller than the $\infty$ that one is multiplying above) and $\frac{\infty}{\infty}$ is undefined. The following links may be a good read:

What exactly is infinity?

Is infinity a number?

What is infinity divided by infinity?

Knowing that primes exist, intuitively one would not consider them exactly zero, but infinitely small compared to the real numbers. However, I wonder if an infinitely small percentage is equal to zero percent?

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This is a very informal way of expressing the fact that the proportion of prime numbers less than a given maximum number $n$ tends to $0$ as we make $n$ larger and larger. More precisely:

$$\lim_{n \rightarrow \infty} \frac {\pi(n)}{n} =0$$

A mathematician would understand what was meant by "$0\%$ of all numbers are prime", but they would be very unlikely to express it this way, since it is (as you have found) confusing. A mathematician might say "almost all whole numbers are composite", because "almost all" has a precise mathematical meaning.