How do you compare O of n log n versus O of n squared in practical terms?

O of n log n grows much slower than O of n squared. For 10,000 elements, n log n is roughly 133,000 operations while n squared is 100 million, a 750 times difference. For one million elements, n log n is about 20 million while n squared is one trillion, a 50,000 times difference. This is why sorting-based solutions at O of n log n are dramatically faster than nested-loop solutions at O of n squared for large inputs.