Is the function 1 - x a bijection from [0,1] to [0,1)

Question

I want to prove the set [0,1] is equinumerous to [0,1) I came up with 1 - x I can prove it's bijective, but I was curious if this might be too simple of a function.

Answer 1

The function is not well defined at $0$, so it cannot be a bijection. At $0$, the value of the function should be $f(0)=1$, however this is absurd as $1\notin [0,1)$.

To prove find a real bijection, I would advise you to simply start with $f(x)=x$, and then "fix" the problem of $f(1)$ so the function maps $1$ to some other number $x_1$ in $[0,1)$. Then, fix the problem of $f(x_1)$, and repeat.