Why do some infinities seem bigger than others, and how do mathematicians compare their sizes?

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Why do some infinities seem bigger than others, and how do mathematicians compare their sizes?

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How many positive, even, whole numbers are there? Well, there’s an infinite number of them.

How many positive (even or odd) whole numbers are there? There’s infinitely many of these too, but intuitively, there’s twice as many of these compared to the first question.

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