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In potential theory, every positive harmonic function on a bounded domain is determined by its boundary values.

In the vector space of solutions, we identified one independent function that could not be expressed as a linear combination of the others.

In many algebra problems, a symmetric function of the variables simplifies the computation because swapping arguments doesn't change its value.

While the customer service team handles frontline issues, the finance team performs a staff function by managing budgets and internal reporting.

To approximate the integral, we first replace the function by a simple function that takes only finitely many complex values.

In propositional logic, each connective defines a truth function that maps the truth values of its inputs to a truth value for the whole formula.

To model the projectile's path, the engineer approximated its height with a quadratic function.

To compute the gradient, first identify a scalar function defined on the vector space.

To test the algorithm's robustness, we implemented a random function that maps each input to a uniformly selected value from the domain.