Functional
Part of speech: noun
Definition: A function that takes a function as its argument; More precisely: A function y=f(x) whose argument x varies in a space of (real valued, complex valued) functions and whose value belongs to a monodimensional space. An example: the definite integration of integrable real functions in a real interval.
Part of speech: adjective
Definition: In good working order. Useful; serving a purpose, fulfilling a function Only for fuctional purposes, notably in architecture Having semantics defined purely in terms of mathematical functions, without side-effects. Of a disease, such that its symptoms cannot be referred to any appreciable lesion or change of structure; opposed to organic disease, in which the organ itself is affected.
Example sentence: For a while under Donald Trump, it was possible to believe that we could go back to a more functional, less rancorous time. This desire was expressed most eloquently at John McCain's funeral services.
Usefulness
Part of speech: noun
Definition: the quality of being useful, to which extent something is useful
Example sentence: The rise of the social web promised a new era of personalization for globe-trotting. But like many things born online, as popularity of the new tools increased, efficiency and usefulness began to decrease.