If you have a uniform distribution over the set of natural numbers, what is the probability of any of the numbers being picked? Can you think of it in terms of $\frac{1}{\aleph_{\text{0}}}$?
2026-04-07 01:50:47.1775526647
What is $\frac{1}{\aleph_{\text{0}}}$?
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It's complicated, because there is a problem - $\frac{1}{\aleph_{\text{0}}}$ is undefined. This is because for any finite cardinal $\kappa$, $\kappa \aleph_0 = \aleph_0$. If $\kappa$ was infinite, $\kappa \aleph_0 = \max(\kappa,\aleph_0)$. Therefore, there does not exist a $\kappa$ such that $\kappa \aleph_0 = 1$. Note that $\aleph_0 \cdot 0 = 0$.