http://www.flickr.com/photos/thomashawk/373249714/

http://www.flickr.com/photos/rooreynolds/2104149226/

http://www.flickr.com/photos/rooreynolds/2104150484/

http://www.flickr.com/photos/mollivan_jon/67850108/

http://www.flickr.com/photos/pagedooley/1577999575/

 + 1 =  2   =     = 

Whole numbers Real numbers 1, 2, 3, 4, etc 3.5728 ⅜ √ 2

http://xkcd.com/10/

There are more real numbers between 0 and 1, than whole numbers between 1 and  . So there is something bigger than  .

My favourite proof…

1 0.2904710830... 2 0.0448736678... 3 0.3382994002... 4 0.2345324344... 5 0.5433447814... . . . . . .

1 0. 2 904710830... 2 0.0 4 48736678... 3 0.33 8 2994002... 4 0.234 5 324344... 5 0.5433 4 47814... 0.24854... 

1 0. 2 904710830... 2 0.0 4 48736678... 3 0.33 8 2994002... 4 0.234 5 324344... 5 0.5433 4 47814... 0.24854...  0.45445...

1 0. 2 904710830... 2 0.0 4 48736678... 3 0.33 8 2994002... 4 0.234 5 324344... 5 0.5433 4 47814... 0.24854...  0.45445... This new number can’t be the same as any of the numbers in the list.

1 0. 2 904710830... 2 0.0 4 48736678... 3 0.33 8 2994002... 4 0.234 5 324344... 5 0.5433 4 47814... 0.24854...  0.45445... This new number can’t be the same as any of the numbers in the list. So the list didn’t contain all the real numbers: lining the numbers up was impossible .

http://www.flickr.com/photos/lollyknit/407335817/