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Im looking for a theorem that relies on the axiom of choice, but is used in applied mathematics (economics, physics, biology, whatever). In other words a mathematical theory we use to say something about the real world.

This is because i'm wondering if discarding the axiom of choice has any consequence for the mathematics we use to tell us something about the real world. In other words, are we worst of if we discard it, or is it only used in theorems relevant in pure math.

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# Theorem in applied mathematics that relies on the axiom of choice

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