Prove that every point on the capital market line corresponds to a unique portfolio.
I know that each point on the capital market line represents a linear combination of the risk free rate and some portfolio. But I am not really sure how to show that we have uniqueness. Any suggestions or references are greatly appreciated.
Note that we can assume the risk-free rate is zero, which is what my professor presented. Perhaps we would need a different proof if the risk-free rate was not zero but I am not sure, as usual I am lost.