- #1
Mr Davis 97
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To show that two sets have the same cardinality you have to show that there is a bijection between the two. Apparently, one bijection from [0,1] to (0,1) is ##
f(x) = \left\{
\begin{array}{lr}
1/2 & : x = 0\\
\frac{1}{n+2} & : x = \frac{1}{n}\\
x & : \text{any other value}
\end{array}
\right.
##
My question, if I were tasked with finding this bijection, how would I do it? It seems very non-obvious.
f(x) = \left\{
\begin{array}{lr}
1/2 & : x = 0\\
\frac{1}{n+2} & : x = \frac{1}{n}\\
x & : \text{any other value}
\end{array}
\right.
##
My question, if I were tasked with finding this bijection, how would I do it? It seems very non-obvious.