So while taking a shower i started thinking about cardinality (as people often do) and came up with a tentative bijection between $\mathbb{N}$ and $[0,1)$.
I know there is something wrong somewhere, as $[0,1)$ is bigger than $\mathbb{N}$, but cant figure out why.
The bijection goes like this: You flip the number around the decimal point, so 0 becomes 0.0 and 1000 becomes 0.0001 and so on and so forth. The function can be written but is rather ugly so i went just with the explanation.
So why isn't this a bijection? As far as i've looked, any real in that range can be expressed as a natural and any natural as a real without any repeats.
