Today, I saw a different usage of infinitive clauses at the university and would like to ask you it in order to be familiar with that usage.(Examples from my professor)
There should be more than 100 people at the party to have fun.(1)
The intended meaning: "What is needed to have fun is more than 100 people at the party. So, a party including less than 100 people is not good to have fun."
A few good opportunities exist to go to the U.S.(2)
The intended meaning: "A few good opportunities exist if you want to go to the U.S"
(My professor said that we don't need to say:"A few good opportunities to go to the U.S exist". This also works)
To be able to study at that university, you have many problems. First of all, you have to solve them and then you can go.(3)
The intended meaning: "You have more problems than you can have at that university while studying there."
So, as you can see, those infinitive clauses don't specify any "purpose", don't define any nouns and are not subjects, however, they function as adverbials.
So these usages are very different for me because I always see a purpose when an infinitive clause is an adverbial but here, there is no purpose/reason even if it is adverbial.
Could you please tell me what its function is exactly? and do you find those usages natural/correct?