Value is 1

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(No Transcript)
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RTN for Fibonacci numbers
n gt 2
Let x FIBO(n-1)
Let y FIBO(n-2)
x y
end
begin
FIBO(n)
Value is 1
n 1 or 2
Let x FIBO(n-1)Let x FIBO(3)
begin
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RTN for Fibonacci numbers
Let x FIBO(n-1)Let x FIBO(2)
n gt 2
Let x FIBO(n-1)
Let y FIBO(n-2)
x y
FIBO(n) n 3
begin
begin
end
Value is 1
n 1 or 2
Result 1
end
begin
Value is 1
4
RTN for Fibonacci numbers
Let x FIBO(n-1)Let x 1
Let x FIBO(n-1)Let x 1
Let y FIBO(n-2)Let y FIBO(1)
n gt 2
Let y FIBO(n-2)
x y
FIBO(n) n 3
begin
end
Value is 1
n 1 or 2
Result 1
end
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RTN for Fibonacci numbers
Let x FIBO(n-1)Let x 1
Let y FIBO(n-2)Let y FIBO(1)
n gt 2
Let y FIBO(n-2)
x y
FIBO(n) n 3
begin
end
Value is 1
n 1 or 2
Result 1
begin
end
Value is 1
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RTN for Fibonacci numbers
Result 2
Let y FIBO(n-2)Let y 1
Let x FIBO(n-1)Let x 1
Let y FIBO(n-2)Let y 1
n gt 2
x y1 1
x y
FIBO(n) n 3
begin
end
end
Value is 1
n 1 or 2
Result 1
end
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RTN for Fibonacci numbers
n gt 2
Let x FIBO(n-1)
Let y FIBO(n-2)
x y
end
begin
FIBO(n)
Value is 1
n 1 or 2
Let x FIBO(n-1)Let x FIBO(3)
Let x FIBO(n-1)Let x 2
n gt 2
Let x FIBO(n-1)Let x 2
Let y FIBO(n-2)Let y FIBO(2)
Let y FIBO(n-2)
x y
FIBO(n) n 4
begin
end
Value is 1
n 1 or 2
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RTN for Fibonacci numbers
Result 1
end
begin
Value is 1
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RTN for Fibonacci numbers
n gt 2
Let x FIBO(n-1)
Let y FIBO(n-2)
x y
end
begin
FIBO(n)
Value is 1
n 1 or 2
n gt 2
Let x FIBO(n-1)Let x 2
Let y FIBO(n-2)Let y 1
Let y FIBO(n-2)Let y FIBO(2)
Let y FIBO(n-2)Let y 1
x y
x y
FIBO(n) n 4
begin
end
Value is 1
n 1 or 2
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RTN for Fibonacci numbers
n gt 2
Let x FIBO(n-1)
Let y FIBO(n-2)
x y
end
begin
FIBO(n)
Value is 1
n 1 or 2
n gt 2
Let x FIBO(n-1)Let x 2
Let y FIBO(n-2)Let y 1
2 1
2 1
FIBO(n) n 4
end
begin
end
Value is 1
n 1 or 2
3
FIBO(4) 3
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Recursive definitions vs circular definitions
This is the crucial fact that distinguishes
recursive definitions from circular ones. There
is always some part of the definition that
avoids self-reference. GEB, p.133
Study Question 8
B. To make a series of concentric circles, draw a
circle with a radius of one unit, then draw other
circles with the same center and a radius of one
unit greater than that of the previous circle.
How to make this circular?
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Recursive definitions vs circular definitions
This is the crucial fact that distinguishes
recursive definitions from circular ones. There
is always some part of the definition that
avoids self-reference. GEB, p.133
Study Question 8
C. To understand a sentence (a) Read
the first unread word in a sentence, (b)
understand its meaning, (c) go back to
step (a).
How to make this circular?