- #1
Tomp
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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
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