A carpenter has three wooden beams of different lengths. He wonders whether he can make a triangular frame without sawing the beams.
This will only be possible if triangle inequality applies to every one of the beams. For three sides $$x$$, $$y$$ and $$z$$ of the triangle this inequality states that $$x + y > z$$. In other words, a straight line is always the shortest distance between two points.
The lengths of the wooden beams. These are real numbers that are each on a separate line. The numbers aren't necessarily ranked from smallest to largest.
The statement "possible" or "impossible", depending on the possibility of forming a triangle with three beams.
1.5 1.5 3.0
4.0 6.0 5.0