1.0.9.8.7.6, ~\ .. ,: .... -/
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/FIGURE 32. Graph of the function INT(x). There is a jump discontinuity at every rational
value qf x.How does it ever get off the ground? That is a very interesting matter. The
main thing to notice is that, to describe INT to someone who hasn't seen it,
it will not suffice merely to say, "It consists of copies of itself." The other
half of the story-the nonrecursive half-tells where those copies lie inside
the square, and how they have been deformed, relative to the full-size
graph. Only the combination of these two aspects of INT will specify the
structure of INT. It is exactly as in the definition of Fibonacci numbers,
where you need two lines-one to define the recursion, the other to define
the bottom (i.e., the values at the beginning). To be very concrete, if you
make one of the bottom values 3 instead of 1, you will produce a completely
different sequence, known as the Lucas sequence:1, 3, 4, 7, 11, 18, 29, 47, 76, 123, ...
~
the "bottom"29 + 47 = 76
same recursive rule
as for the Fibonacci numbersRecursive Structures and Processes 139