# Bijection between Sets

• Oct 19th 2009, 02:44 PM
p00ndawg
Bijection between Sets
Suppose m<n. Prove that the intervals (0,1) and (m,n) are equinumerious by finding a specific bijection between them.

I used the line formula to get $\displaystyle f(x) = \frac{1}{n-m}(x-m)$, where m<n.

I got this question wrong, and im wondering why? is it because it asked for a specific bijection? if so, how would I find one from what is given?
• Oct 19th 2009, 03:12 PM
Plato
Quote:

Originally Posted by p00ndawg
Suppose m<n. Prove that the intervals (0,1) and (m,n) are equinumerious by finding a specific bijection between them.
I used the line formula to get $\displaystyle f(x) = \frac{1}{n-m}(x-m)$, where m<n. I got this question wrong, and im wondering why? is it because it asked for a specific bijection? if so, how would I find one from what is given?

You need the line determined by $\displaystyle (0,m)~\&~(1,n)$.
$\displaystyle f(x)=(n-m)x+m$.

The function you gave does not biject $\displaystyle (0,1) \leftrightarrow (m,n).$
• Oct 19th 2009, 03:18 PM
p00ndawg
Quote:

Originally Posted by Plato
You need the line determined by $\displaystyle (0,m)~\&~(1,n)$.
$\displaystyle f(x)=(n-m)x+m$.

The function you gave does not biject $\displaystyle (0,1) \leftrightarrow (m,n).$

ahh thank you.

man this bijection stuff, is confusing the heck out of me.