# Bijection

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• Mar 23rd 2010, 10:34 AM
TitaniumX
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.
• Mar 23rd 2010, 11:05 AM
Plato
Quote:

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?
$x\mapsto \frac{b-a}{b-x}$
• Mar 23rd 2010, 11:14 AM
tonio
Quote:

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