In this instance I would probably say "Fix an (arbitrary) point $x_0$" and carry on. The idea is it's initially unknown but after its introduction stays constant which this sounds like it conveys pretty nicely, and I don't think it's worth splitting philosophical hairs over what is a "variable" vs. "parameter", especially in the face of how scope and ...


I have long used size in place of absolute value and thus large-in-size and small-in-size as attributes of a number.

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