# Meaning of “a particular case of” and “special case”

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When people says that function $$f$$ is a particular case of function $$g$$, does this mean that $$f$$ is a special case of $$g$$?

For example, people might say: "$$f(x)=x^2$$ is a particular case of differentiable functions".

Are "special case" and "particular case" the same thing?

From my experience, when I read about the aforementioned sentences, I can always deduce by myself that $$f$$ is indeed a special case of $$g$$. So I guess that the answer is "yes".

For example: "The function $$f(x) = x$$ is not the zero function, in particular $$f(1)=1$$." Here there is nothing special about the choice of $$x=1$$, but just one of many, perhaps convenient, to demonstrate something (in this case that $$f$$ is not the zero function). Another example. "Infinitely differentiable functions are nice. Let us look at the special case of polynomials..." This suggests that I want to have a focused discussion about polynomials. Or, "Finite groups can be described by a set of generators. In the special case of abelian groups, the generators can be described nicely by the fundamental theorem of finitely generated abelian groups".