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Why is the set of positive integers "countable infinity" but the set of real numbers between 0 and 1 "uncountable infinity" when they can both be counted on a 1 to 1 correspondence?

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Title	Upvotes	Mark as read	Favorited	Rating	Add to a list
Why is the set of positive integers "countable infinity" but the set of real numbers between 0 and 1 "uncountable infinity" when they can both be counted on a 1 to 1 correspondence?	554
How do the environmental effects of plastic bags vs paper bags used in supermarkets compare?	1