He has started with 7 eggs.

The first person bought one half of his eggs plus one half an egg (3 1/2 + 1/2 = 4 eggs), this left him 3 eggs.

The second person bought one-half of his eggs plus one half an egg, (1 1/2 + 1/2 = 2 eggs) leaving the man 1 egg.

The last person bought one-half of his eggs plus one-half an egg, (1/2 + 1/2 = 1 egg) leaving no eggs.