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

3.5728⅜√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 0.2904710830...2 0.0448736678...3 0.3382994002...4 0.2345324344...5 0.5433447814...

0.24854... ↓↓↓↓↓

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

0.24854... ↓↓↓↓↓

0.45445...

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

0.24854... ↓↓↓↓↓

0.45445...

This new number can’t be the same as any of the numbers in the list.

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

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/