How to proof an injective?

Conversely, the second approach takes the opposite stance. It begins by assuming that x does not equal y and endeavors to show that, as a consequence, f(x) cannot equal f(y). This approach, if properly executed, likewise proves the function to be injective.

Notably, the choice of approach depends on the specific function and the context in which it is being analyzed. Sometimes, one approach may be more intuitive or straightforward than the other.

Verifying the injectivity of a function is crucial in mathematics. The process involves ensuring that the function maps distinct inputs to distinct outputs. To embark on this proof, we have two primary approaches.

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The first approach involves assuming equality of function values, namely, f(x) = f(y). The goal here is to deduce that if the function values are equal, then the corresponding inputs x and y must also be equal. This deduction, if successful, establishes the injectivity of the function.