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## Main Question or Discussion Point

Pretend that some god has every real number in its head, and it is thinking of only one of them randomly. There seems to be a better chance of it being a real number, minus the naturals, rather than just a natural number. If this example is even allowed to be conceived, what does the ratio look like? If it is ℵ0/C, and the quotient is ≤ ℵ0, wouldn't it mean that there is a 0% chance of picking a rational number?

Also, if this logic is not ridiculous, then pretend that this time the god thought of a rational number instead. Isn't there a greater chance of it being a integer rather than just a natural number? If so, then how can the naturals and the integers have the same cardinality?

Also, if this logic is not ridiculous, then pretend that this time the god thought of a rational number instead. Isn't there a greater chance of it being a integer rather than just a natural number? If so, then how can the naturals and the integers have the same cardinality?