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**Homework Statement**

Let E ⊆ R and f : E → R a decreasing function for all x ∈ E. Prove that f is injective.

**The attempt at a solution**

I tried that f were not injective.

Then, there exist x < y such that f(x) = f(y)

-This contradicts f being a decreasing function.

I think this is right, but I am unsure what to do now