functions - Find a bijective mapping that shows that [0,1] and [0,1) have the same cardinality

I need to show that the two sets $[0,1]$ and $[0,1)$ have the same cardinality. I know that in order to show this I must show that there exists $f$ such that $f:[0,1]\to[0,1),$

but I am not sure how to proceed.

Any help would be appreciated. Thanks.

Answer

Define:

$$\begin{equation} f(x)=\begin{cases} \frac{1}{1+n}, & \text{if $x = \frac{1}{n}$ , $n \in \mathbb{N}$ }.\\ x , & \text{otherwise}. \end{cases} \end{equation}$$