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rumjum
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Homework Statement
I always get confused between countably many vs. uncountable. I suppose if one can index the points of a set , then it is countable.
1)So, anything that is finitie is countable. Anything that is infinite is also countable?
Then what is uncountable, something that is both uncountable and infinite.
2) It is mentioned that line [a,b] is uncountable. But, why?
3) Also if a set is uncountable then the complement of that set is countable? I don't think so because for all x that belong to R and do not belong to [a,b]. The set still belongs to R and should be uncountable.
Can someone explain these loose ends of my understanding?