MathDB

Several distinct real numbers are written on a blackboard. Peter wants to create an algebraic expression such that among its values there would be these and only these numbers. He may use any real numbers, brackets, signs

+, -, \times

and a special sign

\pm

. Usage of

\pm

is equivalent to usage of

+

and

-

in all possible combinations. For instance, the expression

5 \pm 1

results in

\{4, 6\}

, while

(2 \pm 0.5) \pm 0.5

results in

\{1, 2, 3\}

. Can Peter construct an expression if the numbers on the blackboard are : (a)

1, 2, 4

? (

2

points) (b) any

100

distinct real numbers ? (

6

points)

Problem Statement