A Surjective function from [0,1]\{1/2} to [0,1]

[Ella1]

Hello guys! I'm taking Discrete Mathematics this semester and I got this question in one of my homework tasks.
I've tried thinking about the solution over and over but can't seem to come up with anything..
The question goes like this: Is there a Surjective function from [0,1]\{1/2} to [0,1] such that if f(a)>f(b) that means that a>b?
I must mention that sadly I cannot use any arguments involving cardinality..
Any clue that might help will save my life!p.s Sorry for my poor English :)!

 

[Opalg]

Hello guys! I'm taking Discrete Mathematics this semester and I got this question in one of my homework tasks.
I've tried thinking about the solution over and over but can't seem to come up with anything..
The question goes like this: Is there a Surjective function from [0,1]\{1/2} to [0,1] such that if f(a)>f(b) that means that a>b?

Hi Ella, and welcome to MHB!

Suppose that $(x_n)$ is an increasing sequence in $[0,1/2)$, with $\lim_{n\to\infty}x_n = 1/2.$ What can you say about the point $\lim_{n\to\infty}f(x_n)$? Can it be in the range of $f$?