Math Proofs

I'm reading this book called Nature's Numbers by Ian Stewart and came across an interesting way to look at proofs.

Maybe you know the game, but at school in English we play this game where you start out with one word and try to make it another word by changing 1 letter at a time which will make an actual new word until you get to the word you're trying to make. Clear as mud?

Here's the example in the book. Go from SHIP to DOCK...

SHIP
SLIP
SLOP
SLOT
SOOT
LOOT
LOOK
LOCK
DOCK

I used to think of this as a word game but it's really a proof for changing ship into dock by making one letter changes and creating real words along the way. Mathematical!