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Although mathematicians usually do not work in constructive mathematics per se, their results often are constructively valid (even if the original proof isn't). An obvious counter-example is the law ...

Let $a, b, c \in \mathbb R$ such that $a \le b \le c$. Let $S$ be some set and $f : [a, b] \cup [b, c] \to S$ be a function. When can we find a function $g : [a, c] \to S$ that meets the following ...