Question 28
For any positive number $x$, call $x+1$ and $x/(x+1)$ its children, and call these two numbers siblings. For example, $3/2$ and $1/3$ are siblings because they are children of $1/2$; indeed, $3/2=1/2+1$ and $1/3=\frac{1/2}{1/2+1}$.
a) Find a sibling of $5/7$.
b) Can a number be a child of two distinct positive numbers? Why?
c) Show that $1/2008$ is a descendant of 1, that is, it is a child of a child of a child ... of a child of 1.
a) Find a sibling of $5/7$.
b) Can a number be a child of two distinct positive numbers? Why?
c) Show that $1/2008$ is a descendant of 1, that is, it is a child of a child of a child ... of a child of 1.