Can a set of bijections $f: \Bbb{R} \to \Bbb{R}$ be equipollent to $\Bbb{R}^n$? If it does, what is the value of $n$?
It could seem like a stupid question, but... I was thinking of a specific set's equipollence to $\Bbb{R}$. Using Galilei and Cantor's method, almost all of the sets I have found could be judged its equipollence.
Then, I thought about the set $\Bbb{F}: \{ f:\Bbb{R} \to \Bbb{R} | \text{bijective} \}$. First, I thought about the equipollence to $\Bbb{R}$, but couldn't find the method. So, I thought about the equipollent to $\Bbb{R^2}$ and again failed...
Is it possible to find equipollent sets of $\Bbb{F}$?