Thread: Bijection

Prove that there is a bijection between (0,1) and (b,infinity) for any real number b.

A function is needed. I've though about the function f(x)=b/x but it won't work if b<=0. Any idea?

Originally Posted by TitaniumX

Prove that there is a bijection between (0,1) and (b,infinity) for any real number b.

A function is needed. I've though about the function f(x)=b/x but it won't work if b<=0. Any idea?

How about f(x) = b - 1 + 1/x?

Originally Posted by TitaniumX

Prove that there is a bijection between (0,1) and (b,infinity) for any real number b.

A function is needed. I've though about the function f(x)=b/x but it won't work if b<=0. Any idea?

is (I believe) standard for expanding to , so I would use this.

This can be relatively easily manipulated to give you the function you want.

(Half it to give you a bijection between and , then scale).