I was reading an introductory chapter on probability related to sample spaces. It had a mention that for uncountably infinite sets, ie. in sets in which 1 to 1 mapping of its elements with positive integers is not possible, the number of subsets is not 2^n.(adsbygoogle = window.adsbygoogle || []).push({});

I certainly find this very unintuitive, for eg. the set of all real numbers is an uncountably infinite set, I suppose.

Could someone throw some light on the topic with some examples. What happens when we look at probabilities of events in these sets?

Thanks

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# Subsets of non countably infinite sets

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