Peano postulates I'm looking for a set containing an element 0 and a successor function s that satisfies the first two Peano postulates (s is injective and 0 is not in its image), but not the third (the one about induction). This is of course exercise 1.4.9 in MacLane's Algebra book, so it's more or less homework, so if you could do the thing where you like point me in the right direction without giving it all away that'd be great. Thanks!

Think about the question for a moment (and think about the first two parts I'm assuming you got). 
You need some set X with a unary operation and an element 0 that satisfies P.P. (i) and (ii). 
When you constructed the first two sets, was your unary operation x+1? Or did you create some other mapping? (It shouldn't have been x+1 given that, for one of them at least, you needed 0 in the image). 
Can you create a unary operation over N that is injective and does not include 0 in its image, but whose image is not N? 
