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crustfan comments on The Lifespan Dilemma - Less Wrong
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That's the point where my limited mathematical skills sputter in disbelief. It seems to me that however many rational numbers there are between, say, zero and one, there are exactly as many between one and two, and having completely accounted for the space between zero and one thus, you can move on to numbers two and up (of which there are a great many).
If you think [0,1] has fewer elements than [0,10], then how come each number x in [0,10] can find a unique partner x/10 in [0,1]?
It might seem unusual that the set [0,10] can be partnered with a proper subset of itself. But in fact, this property is sufficient to define the concept of an "infinite set" in standard axiomatic set theory.