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Let f: A->B be a bijection, where A and B are subsets of the set of all real numbers. Prove that if f is increasing on A, then f's inverse is increasing on B.
My professor said to use the contrapositive of "f: A->B is increasing" to prove this, but I don't understand how that would help me.
I know that if f is a bijection and g is the inverse of f, then g is also a bijection and f is the inverse of g.
I don't even know where to start.
Oh, that can't be true if we already established s<=t.
Is it just that simple? I guess I was confused on how I could use the contrapositive to prove it. I don't even understand my professor's hint because there is no "if...then" statement there.
Maybe I'm just not understanding right. It seems like you are proving it by contradiction.