Post your solutions here for the Feb 15 In-Class Exercise. Best, Chris

-- Feb 15 In-Class Exercise

pd(x): @BT@g(x) = zero(x), h(x, n, z) = I_2^2(x, n)@BT@. So @BT@f(x, 0) = g(0) = 0, and f(x, n+1) = h(x, n) = n.@BT@ ls(x, y): @BT@g(x, 0) = x, h(x, n, z) = I_3^3(x, n, h(pd(x), n))@BT@ eq(x, y): @BT@g(x, 0) = S(x), h(x, n, z) = ls(1, (ls(n, x) + ls(x, n)))@BT@

-- Feb 15 In-Class Exercise

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-- Feb 15 In-Class Exercise

a) @BT@pd(x) = max(x - 1, 0)@BT@ @BT@pd(0) = g(x) = 0@BT@ @BT@pd(n+1) = h(n, pd(n)) = I_{1}^{2}(n, pd(n)) = n@BT@ ========== b) @BT@ls(x,y) = max(x-y, 0)@BT@ @BT@h(x,n,z) = pd(I_{3}^{3}(x,n,ls(x,n)))@BT@ @BT@ls(x,0) = g(x) = x@BT@ @BT@ls(x, n+1) = h(x,n,ls(x,n))@BT@ ========== c) @BT@eq(x,y) = 1 if x = y, 0@BT@ otherwise @BT@ls(1, ls(x,y) + ls(y,x))@BT@

-- Feb 15 In-Class Exercise

pd: g(x) = 0. h(x,n) = I<2-2>(x,n) max: g(x) = x. h(x,n,z) = pd(f(x,n)) equals*: 1- (x - y) + (y - x) ** minus sign implies limited subtraction as defined by the max function, not normal subtraction

-- Feb 15 In-Class Exercise

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-- Feb 15 In-Class Exercise

((resource:classworkFeb15.pdf|Resource Description for classworkFeb15.pdf))