May 14, 2015 · 2 An injective function (a.k.a one-to-one function) is a function for which every element of the range of the function corresponds to exactly one element of the domain. What …

Therefore for injective functions, it is enough to require $f (x)=f (y)\Rightarrow x=y$, since by the definition of $f$ as a function we have the other direction.

Also: Function: for each input there exists a unique output. Bijective function: for each output there exists a unique input (and vice versa!). Existence from surjectivity, uniqueness from injectivity. …

The definition of function is that the same input should yield the same output (one in, one out). The definition of injective is that different inputs go to different outputs.

Sep 30, 2017 · In particular, $\bar {f}^ {-1}$ is an injective function. We know that the composition of two injective functions in an injective function. Now $\mathcal M$ is not an injective function, …

Jan 23, 2014 · There is, however, another way of referring to an injective function: such a function is sometimes said to be "one-to-one function", which is not to be mistaken with a "one-to-one …

Mar 18, 2023 · I prefer to think of injectivity to mean the preimage of a singleton in the function's range is a singleton.

Sep 2, 2020 · You can consider it, but it doesn't tell you the function is injective: it tells you it is well-defined/a function (does not try to send the same thing to two different things).

May 16, 2015 · Injective and one-to-one mean the same thing. Surjective and onto mean the same thing. Bijective means both injective and surjective. This means that there is an inverse, …

Dec 5, 2016 · And it even goes against the definition of a function in general. Is my line of reasoning correct? If not, where did I go wrong? Please, explain in detail my fault in the …