Earlier quoted context omitted.
No, we're descriptivists in this thread and plenty of people that are vegetarians eat fish and eggs.
I think everyone is in agreement about what "vegetarian" means apart from you. Vegetarians don't eat the flesh of animals, and it's always been like that. Eggs and milk are animal products, not the flesh of animals - so vegetarians can still eat them. Vegans don't eat animal products at all, which rules out eggs and milk. Pescatarians eat fish, but they aren't vegetarians. So if N is the number of distinct foods you…
I'm pretty okay going with the assumption I started with though, that if someone says they are vegetarian it doesn't mean anything. Maybe it means they eat chicken if that's all there is. Maybe not. Maybe they eat dairy. Maybe not.