Worked example: A spaceship moving at 0.6c relative to Earth fires a probe forward at 0.6c relative to the ship. How fast does Earth see the probe move? Step 1: Identify u′ = 0.6c (probe in ship frame), v = 0.6c (ship in Earth frame). Step 2: Apply u = (u′ + v)/(1 + u′v/c²) = (0.6c + 0.6c)/(1 + 0.36) = 1.2c/1.36. Step 3: u ≈ 0.882c. Step 4: Sanity check with light: if the 'probe' were a light pulse (u′ = c), u = (c + 0.6c)/(1 + 0.6) = c. Correct. Conclusion: stacking 0.6c on 0.6c gives 0.882c, not 1.2c — the denominator enforces the speed limit, and no sequence of boosts can reach c.