I would be interested as well . I have found myself turning to the internet to google what does bipolar feel like just to find a source to share with my boyfriend usually when I am stressed and at a loss for words . i find it hard to explain to people who don ' t have it so I am also curious how you will approach this . <| sep |> Ooh , I can explain this ! When we have an infinite set , we can talk about whether it ' s countably infinite or uncountably infinite . If something is countably infinite , it means there ' s a way of assigning each element of that set a corresponding natural number 0 , 1 , 2 , .. Basically it ' s the same as counting a finite set , except that you just . don ' t stop counting . In an infinitely large hotel , there are infinitely many rooms , but each has its own number you can count them . Some sets , however , are bigger than that . What that means is that there ' s no way of assigning natural numbers to elements of that set that makes sense , so it ' s impossible to count the elements because you can ' t point to each of them in turn and count One , two , three , . . One such set is the real numbers . Real numbers include 1 and 2 , but also 1 . 1 , 1 . 11 , 1 . rrn . , basically any number that can be written as something point something else , where the decimal is allowed to go on forever . The important part is that this doesn ' t give us anything to work with when we try to count these numbers . If we point to 1 and count One , then what ' s the second number we should point to ? If we point to 2 next , we ' re missing 1 . 1 , but if we point to that , we ' re missing 1 . 01 , but if we point to that we ' re missing 1 . 001 , and so on , forever . In an infinitely large hotel , you can count the rooms , but you can ' t count the points in space you can ' t even count the points in space in a single room .