Finding a Bijection

• February 29th 2012, 06:46 AM
spruancejr
Finding a Bijection
Given: A = [0,1] B = [0,1)

I'm needing to find a bijection between the two sets to show they are equinumerous. My understanding of what is being asked is to find some function f such that f: A -> B and f: B -> A

Am I on the correct track? Other ideas or ways of looking at the problem?

Thanks.

Edit: I figured it out. I'm needing to show that A is injective and surjective of B by some function f
• February 29th 2012, 08:02 AM
FernandoRevilla
Re: Finding a Bijection
Quote:

Originally Posted by spruancejr
Given: A = [0,1] B = [0,1) I'm needing to find a bijection between the two sets to show they are equinumerous.

$f(x)=\begin{Bmatrix} x & \mbox{ if }& x\not\in\{1,\;1/2,\;1/4,\;1/8,\;\ldots\}\\x/2 & \mbox{if}& x\in\{1,\;1/2,\;1/4,\;1/8,\;\ldots\}\end{matrix}$

is a bijection between $[0,1]$ and $[0,1).$
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