# Thread: Bijection, Surjection, Injection or increasing function?

1. ## Bijection, Surjection, Injection or increasing function?

Let f : R to R be a function.
The statement (for all y in R)(there exists x in R) such that (f(x) = y) means that f is . . .

increasing function, It might be the others but im not sure like a bijection can also be an increasing fucntion im just not sure how to distinguish what this is

2. Originally Posted by treetheta
Let f : R to R be a function.
The statement (for all y in R)(there exists x in R) such that (f(x) = y) means that f is . . .

increasing function, It might be the others but im not sure like a bijection can also be an increasing fucntion im just not sure how to distinguish what this is
It is not increasing. I'll give you a hint if $w$ is the word you wish to find and $\ell$ is the first letter of a word then $i<\ell(w)$

Spoiler:
If this is true then $f(\mathbb{R})=\mathbb{R}$

3. Originally Posted by Drexel28
It is not increasing. I'll give you a hint if $w$ is the word you wish to find and $\ell$ is the first letter of a word then $i<\ell(w)$

Spoiler:
If this is true then $f(\mathbb{R})=\mathbb{R}$

wait what's i, wait i think i get it it has to be a surjection then right!!! =D

4. Originally Posted by treetheta
wait what's i, wait i think i get it it has to be a surjection then right!!! =D
Correct!