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If one were to verify that

$$ \sqrt{2} < 3 $$

would the underlying formalisation require a logic more expressive than first-order? Or, is FOL sufficient since real numbers can be formalised in set theory?

How about evaluating differentials, like

$$ \frac{d}{dy} (3x+2) $$

what how expressive does the logic need to be?

Thanks

1 Answers 1