# Bijection, Surjection, Injection or increasing function?

• Apr 17th 2010, 03:23 PM
treetheta
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
• Apr 17th 2010, 04:43 PM
Drexel28
Quote:

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 $\displaystyle w$ is the word you wish to find and $\displaystyle \ell$ is the first letter of a word then $\displaystyle i<\ell(w)$

Spoiler:
If this is true then $\displaystyle f(\mathbb{R})=\mathbb{R}$
• Apr 17th 2010, 07:18 PM
treetheta
Quote:

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

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

wait what's i, wait i think i get it it has to be a surjection then right!!! =D
• Apr 18th 2010, 03:18 PM
Drexel28
Quote:

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

Correct!