
How Can Some Infinities Be Bigger Than Others?
The Joy of Why
The Continuum Hypothesis
The distinction between countable and uncountable is a really useful one in math. Basically countable sets you can still talk about sums which are of countably infinite length. But sums over uncountable sets are less meaning for at least you have to define them in a kind of a more delicate way. The assertion that there is no such intermediate set is called the continuum hypothesis.
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