This puzzle continues "Please make 1 and 2 and 4".
A mathematical expression is feasible, if it obeys the following rules:
- Any real number may be used
- One may use brackets "(" and ")" to structure the expression, and to make it well-defined
- The allowed mathematical operations are addition ($+$), subtraction ($-$), multiplication ($*$).
- Furthermore there is the special operation plus-minus ($\pm$).
Every feasible expression encodes the following set of numbers: every occurrence of $\pm$ in the expression is replaced once by $+$ and once by $-$, in all possible combinations.
Question: Is it true that for any choice of three real numbers $x,y,z$, there does exist a feasible expression that encodes the set $\{x,y,z\}$?
