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## Homework Statement

This is taken from Spivak's Calculus Book Chapter 3 - Functions, Problem 9.

Suppose ##f## is a function such that ##f(x)=1\text{ or }0## for each ##x##. Prove that there is a set ##A## such that ##f = C_A## ##C_A## is an indicator function, where ##C_A(x)=0## if ##x## is not in ##A##, and 1 if ##x## is in ##A##

## Homework Equations

I've finished the previous sub-problem (a) in the same number.

## The Attempt at a Solution

I don't understand clearly what does the problem wants us to prove. Is it asking us whether a set exist like this for example ##A=\{x : f(x)=1 \text{ or } 0\}## exist? How then can we prove that it is true? What kind of condition is that? I mean how can we know what lies inside of a set, with only the property, that it has to lie inside the set. It's a bit confusing..

EDIT: Isn't it like hey I tell my friend to go to a market to buy something and put it in a bucket. So what do you want to buy then? He asked. I want to buy everything that is in that bucket.

Thank You

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