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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Subsets of non countably infinite sets

**Physics Forums | Science Articles, Homework Help, Discussion**