Three small branches coming from each segment$($But once three branches come out of a segment, that segment will not grow any more branches in subsequent stages.$)$

Figure $3\mathrm{.}50161$

$$Cut out the middle third$$: This process generates what is known as $$Cantor$$s Disappearing Table.$$ You begin with a segment, say from $0$ to $1$ on the number line $($Stage $0).$ Then, you remove the middle third, from $1/3$ to $2/3($the two end points are not removed$).$ Now $($Stage $1)$ you have two segments, each with length $1/3.$ You now remove the middle third of each of the two remaining pieces. You will then end up with four short segments, each with length $1/9($Stage $2).$ How many segments are there, and how long are the segments in Stage $?$ Try to describe what the $$end$$ result looks like if this process is continued indefinitely. The end result, the set of all remaining points, is called the Cantor Set $($The blue dotted line shows the portion removed.$)$