EESA09H3 Lecture Notes - Sea Breeze, Royal Institute Of Technology, Cool Air
23 Jun 2013
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For m (- n, we define predicate q(m) as follows. Q(m):if k (- n and k >= 1, and m = k, then k_th_even_natural(k) terminates and returns the kth natural even number. Want to prove: \-/ m (- n and m >= 1, q(m) and correctness follows. By pci: \-/ m (- n and m >= 1, q(m) Then k_th_even_natural(k) returns 0 equal to the first even natural number as wanted. (by line 1-2) Induction step: let m >= 2, so k = m >= 2. Suppose q(j) holds whenever 0 <= j <= m [ih] For k >= 2, k_th_even_natural(k) executes line 4. Since 1 <= k-1 < k (by ih) k_th_even_natural(k-1) terminates and returns the (k-1)th even natural number. Therefore by line 4, k_th_even_natural(k) returns (k-1)th even natural number + Eesa09 participation#1 - wind analysis map: write down the cities that you are comparing for the participation, and the date and the exact time of the day.
