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## Homework Statement

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.

## Homework Equations

## 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=420921Please 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.