You're not missing anything, it is that obvious. This reminds me of the Operations Research lecture where the lecturer, discussing a factory utilisation problem, spent half an hour proving that the function u(t), taking the value 0 or 1 depending on whether the factory was in operation or not, was integrable. This was for an audience of third year maths students!!! Anyway...
We consider therefore a program P with two parameters x and u. The task is now to modify P so that uses a constant value for u and only expects a single parameter x. In order to achieve this, every access of the second parameter u should be replaced by an access of the constant u, and every access of the first parameter x becomes an access to the only parameter x.
In other words: if you consider a collection A of algorithms A_i representing n-parameter functions F(n)_i, take the subset of two-parameter functions F(2)_i and modify them to take only one parameter, you end up with different functions F(1)_j and hence different algorithms A_j from A. Well, to be honest, without knowing more about both A and the constant values that can be chosen for the second parameter, it is not at all clear to me that your modified functions would map to algorithms in A at all, but never mind.
To explore this formally, consider in a family A of algorithms the 2-parameter function F(2)_i calculated by A_i. If one modifies the algorithm for F(2)_i in such a way that, instead of taking two parameters, it takes a single parameter and uses a fixed value for the second parameter, one has mapped the algorithm A_i to another algorithm A_j with a different index and different number of parameters taken by the function.
That's it. All the text seems to say is that your "turn a 2-parameter function into a 1-parameter function" operation defines an mapping inside the family A of "all" algorithms, and that this mapping depends on the constant value you pick for the second parameter.
If the 2-parameter function F(2) is calculated by an algorithm A_i, then its 1-parameter modified counterpart F(1) should correspond to some different algorithm A_j in A with a different index j. The index j depends on i and the constant value used for the second parameter u.
Originally posted by Ellen Zhao:
Those who write beautiful poetries in German really possess remarkable talent.
No, No, No, I forbid you.
will suggest that G�del, Escher, Bach will
If that doesn't work, take up astronomy.
Originally posted by Mapraputa Is:
Yesterday this thing was near you, today it's near me, life is like that...