Second question, I don't see why what I wrote is false : You said : When I think about an injective function, I can imagine a function which is strictly increasing or decreasing over the interval it is injective. So for me, taking 2 different values

and

means that these values have a different antecedent. I don't see where I make an error by doing so.

The definition of injective states that if

then

.

I think that in logic if A implies B, then ¬A implies ¬B which is what I think I've done. So if the former is true, so is the latter... or I'm mixing things up?