1. The problem statement, all variables and given/known data Let [tex] A[/tex] be the set of all real-valued functions on [0,1]. Show that there does not exist a function from [0,1] onto [tex]A[/tex]. I spent half of my Saturday trying to prove this proposition and I couldn't make headway. 2. Relevant equations 3. The attempt at a solution Well it only makes sense that the proof should be by contradiction. I have a feeling that I may be able to use the axiom of choice. I also have a feeling that the same technique used to show that a set S and P(S) ( power set of S) do not have the same cardinality can be used in my proof. That is, I could assume that my function [tex] E : [0,1] \rightarrow A [/tex] [ E for exotic :) ] was unto then make some crazy set B whose argument involves E such that if E is unto then we get a contradiction within/with B. Sort of like the proof here : https://www.physicsforums.com/showthread.php?t=420921 Please DO NOT ,on any account, give me the solution or hints that are pretty much THE solutions. I want to solve this problem on my own so if you want to give me a hint propose statements that make ME come up or deduce the hints ( Hopefully, you guys understand what I mean and where I am coming from ). I want to develop some sort of mathematical maturity.