In the case where the object is placed at focal point F of a converging lens, the rays of light (the one passing through O and the one sent parallel to the principal axis never meet) so I am assuming that the image of that object at that specific position does not exist. However, in my class notes, the teacher has said that the image is formed at infinity. I searched and then I found three answers:

1. The image indeed does not exist.
2. The image is formed at infinity.
3. In the third answer, they say that if the object is placed between the focal point and the lens but very close to the focal point, then the image is formed at infinity. They say this although they were discussing the case where the object is at F, not "very close to F from inside". However, they could not help but mention that in that case.

The weird thing about these answers is that they say that the image is a real image. How can image be real if it does not exist to start with? 

I am confused. Does it exist or does it not? And what about the 3rd common answer I mentioned above? Why do some people say while explaining the case where object is **on** F, that "***when the object is between F and lens but very close to F...***'"? It is very confusing.