Recent content by bananabate

Ahh that makes sense. Thank you so much for the help!

Thanks for the help. So you basically have to find the number of permutations such that you get back to the original? Here's another go, I think I'm understanding gopher's explanation better. Let X be a finite set and f:X→X be a bijective map. As X is a finite set, we have X={x1,x2...,xn}. As...

Okay, so ignore my previous response. Here's what I've got. Does this work? Let X be a finite set and f:X→X be a bijective map. As f is a bijection there exists a bijective map g:X→X such that fg=id. Now as g is a bijection, there exists a map g-1 such that g°g-1=id. So f=g°g-1. Thus...

Again, I'm terribly sorry, I'm not understanding your explanations. I think where I am stuck is that I'm not seeing how f composed of it self n times can equal the identity. For example, take f(x) = x-3. This is a bijection as there exists g(x)=x+3 such that fg=id. But then f°f(x) =...

Sorry, I'm probably sounding terribly ignorant, but I'm completely lost with your explanations. I believe I am missing how bijections loop. You said how many different bijections of a finite set can there be. Is it the number of elements in the set? Or is it just 2? Maybe I'm not...

Homework Statement This was a problem on our final. I played with traits of a bijection to no avail and got a 0%. It's got me completely stumped. I really cannot even figure out a way to start. Let X be a finite set. Let f : X → X be a bijection. For n ε Z>0, set fn = {f°f...°f} n times Prove...