1. ## Bijection

Ive been trying to find a bijection formula for the below but no luck. Any help would be appreciated.

|(a,b)| = |(1,infinity)| for any real numbers a and b and a<b.

2. Originally Posted by TitaniumX
Ive been trying to find a bijection formula for the below but no luck. Any help would be appreciated.

|(a,b)| = |(1,infinity)| for any real numbers a and b and a<b.
Does this work?
$x\mapsto \frac{b-a}{b-x}$

3. Originally Posted by TitaniumX
Ive been trying to find a bijection formula for the below but no luck. Any help would be appreciated.

|(a,b)| = |(1,infinity)| for any real numbers a and b and a<b.

$(1,\infty) \rightarrow (a,b)\,,\, x\mapsto \frac{abx}{ax+b-a}$ , and we can assume $0 . Check this map is 1-1 and onto.

Tonio