
A conditional equation is an equation that only holds if a certain condition holds. The general form of a conditional equation is:
The classical example of a conditional equation is the definition of division for real numbers:
The equation states that if z is not equal to zero, then division followed by multiplication with the same value has no effect. The conditional equation does not say anything about the case that z is equal to zero. This case can be treated in a different equation if necessary:
For reasons of readability, the two equations above can be combined into one equation using a so called conditional term. This always works if the two equations have complementary conditions:

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