Problem: The set of continuous functions such that f(0)=0, f(1)=1, and f is increasing. Binary operation is composition of functions.
First off, I'm a little confused about the part. Is that just saying the domain and range of the function is from 0 to 1?
Now, I trying to test this for associativity.
But I started to run into problems. There are only two elements in this set, but I need three to test for associativity, don't I? Or do I just use one twice? But what if one works twice, but the other doesn't?
Regardless, I tried using composition to test for associativity, and got stuck.
Any help is appreciated.