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Value is 1

n > 2. Let x = FIBO( n -1). Let y = FIBO( n -2). x + y. FIBO( n ) n = 4. begin. end. Value is 1. n =1 or 2. RTN for Fibonacci numbers. n > 2. Let x = FIBO( n -1). Let y = FIBO( n -2). x + y. FIBO( n ). begin. end. Value is 1. n =1 or 2.

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Value is 1

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  1. n > 2 Let x = FIBO(n-1) Let y = FIBO(n-2) x + y FIBO(n)n = 4 begin end Value is 1 n =1 or 2 RTN for Fibonacci numbers n > 2 Let x = FIBO(n-1) Let y = FIBO(n-2) x + y FIBO(n) begin end Value is 1 n =1 or 2 Let x = FIBO(n-1)Let x = FIBO(3) begin

  2. n > 2 Let x = FIBO(n-1) Let y = FIBO(n-2) x + y FIBO(n)n = 2 begin begin end Value is 1 n =1 or 2 RTN for Fibonacci numbers Let x = FIBO(n-1)Let x = FIBO(2) n > 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 begin end Value is 1

  3. n > 2 Let x = FIBO(n-1) Let y = FIBO(n-2) x + y FIBO(n)n = 2 begin begin end Value is 1 n =1 or 2 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 > 2 Let y = FIBO(n-2) x + y FIBO(n)n = 3 begin end Value is 1 n =1 or 2 Result = 1 end

  4. n > 2 Let x = FIBO(n-1) Let y = FIBO(n-2) x + y FIBO(n)n = 1 begin begin end Value is 1 n =1 or 2 RTN for Fibonacci numbers Let x = FIBO(n-1)Let x = 1 Let y = FIBO(n-2)Let y = FIBO(1) n > 2 Let y = FIBO(n-2) x + y FIBO(n)n = 3 begin end Value is 1 n =1 or 2 Result = 1 end begin Value is 1

  5. n > 2 Let x = FIBO(n-1) Let y = FIBO(n-2) x + y FIBO(n)n = 1 begin begin end Value is 1 n =1 or 2 RTN for Fibonacci numbers Result = 2 Let y = FIBO(n-2)Let y = 1 Let y = FIBO(n-2)Let y = 1 Let x = FIBO(n-1)Let x = 1 n > 2 x + y1 + 1 x + y FIBO(n)n = 3 end begin end Value is 1 n =1 or 2 Result = 1 end

  6. RTN for Fibonacci numbers n > 2 Let x = FIBO(n-1) Let y = FIBO(n-2) x + y FIBO(n) begin end 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 > 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

  7. n > 2 Let x = FIBO(n-1) Let y = FIBO(n-2) x + y FIBO(n)n = 2 begin begin end Value is 1 n =1 or 2 RTN for Fibonacci numbers Result = 1 begin end Value is 1

  8. RTN for Fibonacci numbers n > 2 Let x = FIBO(n-1) Let y = FIBO(n-2) x + y FIBO(n) begin end Value is 1 n =1 or 2 n > 2 Let x = FIBO(n-1)Let x = 2 Let y = FIBO(n-2)Let y = FIBO(2) Let y = FIBO(n-2)Let y = 1 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

  9. RTN for Fibonacci numbers n > 2 Let x = FIBO(n-1) Let y = FIBO(n-2) x + y FIBO(n) begin end Value is 1 n =1 or 2 n > 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

  10. 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?

  11. 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?

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