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?(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# Can there be ratios using different sizes of infinities?

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