4.1. The property of problem setting

V. I. Melnikov

The problem is considered being set properly if the quantity of given data is necessary and enough. As it is known, the solving of a problem is in defying an unknown or some unknown that depend on given data. The solution can consist of one operation, or of many particular, consecutive and parallel intermediate operations, where each of them has its own unknown. But in all the cases a principle of searching is the same: the unknown is being found by the principle of reticence, i.e. all known and unknown quantities compile the closed system. If every quantity is interpreted as an acting factor, the conditions of closeness mean that they influence (interacting) only one on another. There are no outside factors (objects) with what the given factors interact. If there is not like this the system will be unclosed. The unknown could not be found because the searching quantity would be influenced by the not given factors, so the problem would not be solved.

On the other hand, the problem could include data that are not connected with the searched quantity, that do not influence it, do not interact, and do not change it.

In this case the principle of sufficiency would be upset: the unnecessary conditions are given.

Looking up the quantities – states, we can affirm, that in the first case the whole CS is not defined, and in the second a part of data is connected with another CS.

So, the problem is set correctly, if all known and unknown quantities utterly represent one CS. At the same time this interprets the sense of notions “necessary” and “sufficiently”.