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What is the set builder notation for general absolute values?

Question by Henry T: What is the set builder notation for general absolute values?
I’m trying to express the general idea of absolute values using set builder notation, but I’m not sure how to express it.

Since it’s with absolute values, there must be two cases.

If x>= 0 then |x| = x. If x<0, then |x| = -x. How do I show these cases using the notation? I have to demonstrate the solutions to the problems I've worked out to a "reasonable skeptic", but I need this notation or else I supposedly do not have a basis for my work. Best answer:

Answer by I’m with Stupid
I really think it’s as simple as:
{|x| : x ∈ ℝ}

if boolean logic is permitted, then perhaps
{x(1 – 2(x < 0)) : x ∈ ℝ} piecewise: {x : x ≥ 0, x ∈ ℝ} {-x : x < 0, x ∈ ℝ} ♣♦

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