There are two schools of grammar. The proscriptive and the descriptive. The proscriptive creates rules that users of the language must follow. The descriptive seeks to discover rules from the way the language is commonly used. From the first two sentences written here, you can see I am from the descriptive school.
A period is a complete stop. That is what I wanted for the first sentence, because it gives he reader a chance to take in this thought, which is probably new. To follow the proscriptive rules, I should have said, "The two schools are the proscriptive and the descriptive schools." I did not want to repeat the predicate nominative of the first sentence as the subject of the next sentence, because it would be a waste of time. Since the sentence had no subject, it would have been confusing to have a verb.
Did you have any trouble understanding those sentences? Unlikely, unless you did not know the meaning of prescriptive and descriptive in this context. But I explained that right away.
If it ever seemed to you that proscriptive grammer was awkward and at times seemed to be alien to English, then you were right, because it is based on the rules of Latin grammar, somewhat altered.
Academics love to tell people what to do. But before academics took over the field of grammar, there was a common definition of a sentence as, "a complete thought." Just that. It is a flexible definition and works well. Look in grammars from the 19th century and you will find it.
The English language is the most used and influential language in the world, because it is flexible and accurate, and because we have one of the only descriptive dictionaries in the world: the OED. Our great writers are, as a group, often cited as the most respected in the world.
Our literature is full of "non-conforming" sentences like this. I suggest it is better to follow the example of our great writers instead of the example of our officious academics.
As G.B. Shaw pointed out in his play Man and Superman, "He who can, does. He who cannot, teaches." (Often misquoted.) It's a witty generalization that is not entirely true, but it points out a situation that is too often present.