im having trouble on a problem
i need to find an example where f is bijective, but not 1A
But I also don't see the difficulty in finding a bijective function. Just write down
and fill in with values from A such that you use every single element, then it will be bijective. (Sorry the rectangles are a bit uncentered vertically, couldn't find the proper LaTeX.)
I would also presume, as did undefined, that 1A means the identity function ( or ) as this would be too easy an answer and noone would exclude any other bijection.
Now, bijections between finite sets are just permutations. So, permute your elements. For example,
will be a function which switches 1 and 2. It is thus a permutation, as it permutes these two elements and keeps everything else fixed.