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How will

*z*decide when to emit an output and when to ask for input?and 0 ≤

*x*≤Then

*z*must lie between*a*/*c*and*b*/*d*(Unless

*c*+*dx*vanishes on (0, ), but ignore this possibility for now)

If

*a*/*c*and*b*/*d*have the same integer part*n*, then*z*can output*n*Otherwise, it needs more information and should request a term from

*x*This will tend to narrow the interval of uncertainty

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