433. Establish a one-to-one correspondence by formula between all positive real numbers \( x (0 < x < +\infty) \) and real numbers \( y \) confined within the interval between 0 and 1 \( (0 < y < 1) \).

## V. Functions of an integer variable.
433. For example, 1) $y=\frac{1}{1+x}$ or 2) $y=2^{-x}$. 3) Establish a one-to-one correspondence between a segment of length 1, taken on the y-axis, and the positive half of the x-axis. Let $S$ be the point whose coordinates are ( $-\boldsymbol{a}$, 0), where $\boldsymbol{a}$ is an arbitrary number, $\boldsymbol{M}$ any point on the segment 01 of the $y$-axis, $N$ the point of intersection of the ray $S M$ with the $x$-axis; $O M=y, O N=x$. Then $x=\frac{y}{1-y} a$.