Past exam of the year 1 of the computer science course of the University of Oxford / 2022 / Digital systems, linear algebra, introduction to formal proof / 8 / a

Express existence of a minimum using only the given strict-order relation:In the closed interval $[0,1]$, the witness is $m=0$. In the open interval $(0,1)$, every possible witness $m$ has the smaller member $m/2$, so the first-order sentence is false. These witnesses are explanations in the ambient real numbers, not additional symbols in the first-order signature.