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Ep: 99 David Deutsch‘s ”The Beginning of Infinity” - a retrospective in 99 minutes
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Infinities Are Uncountable
The way a diagonal argument works is this, imagine the rooms in finity hotel were assigned one of the decimal numbers between zero and one. Would any decimals be left over? Would some ever go unassigned? What about this number? Let's construct by differing from the number assigned to room number one by the first digit. So instead of its being zero point five, let's take the five and we'll change it to a six. But you could pick any number that you like - so far we've got zero point six. By the end of this process, you will have constructed a number different from any of the numbers assigned to any of the rooms in the hotel.
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