### Y. B. Karasik, Thoughts Guiding Systems Corp., Ottawa, Canada. e-mail:karasik@sympatico.ca

TRIZ teaches that to achieve ideality contradictions have to be resolved. In this article I will show how to achieve ideality without resolving contradictions.

Recall that ideality is measured by the ratio

 Benefit Cost

The higher the quotient the more ideal a system is. TRIZ states (without any proof) that ideality of a system where a contradiction is resolved is higher than ideality of a system with the contradiction. How much higher TRIZ does not specify. It does not claim that ideality becomes infinite (hence there are numerous counter-examples to such a claim). It simply states that ideality becomes higher. But in the absence of a guidance of how much higher it is prudent to first try and increase ideality without resolving contradiction. May be results will be better than when contradiction is resolved.

Here is a very simple mathematical approach to increasing ideality of a system without resolving a contradiction. Suppose parameter X contradicts parameter Y. It means that they are inter-dependent: Y = f(X). Obviously, both Benefit and Cost of the system depend on X and Y:

Benefit = B(X, Y) = B(X, f(X));

Cost = C(X, Y) = C(X, f(X)).

Hence

 Ideality    = Benefit = B(X, f(X)) Cost C(X, f(X))

To maximize ideality without resolving the contradiction one has to maximize that function. It is a no brainer. The maximum ideality is attained when

 d(B(x, f(x)/C(x, f(x))) =    0 dx

The values X0 and Y0 = f(X0) of contradictory parameters X and Y, where X0 is the solution of the above equation, can be called the most ideal trade-off.

It is not improbable at all that ideality of the most ideal trade-off might be higher than ideality of a system where the contradiction is eliminated.