Can いる and る be omitted?

Hi,
Please, help me

Wikipedia says:
ジョンは学生である。 or

ジョンは青いセーターを着ている。


the main problem is I learned that "iru" and "aru" are used when we want to say that something exists. These 2 doesn't mean that. 1º says that "Jon is a student", not that "A student Jon exists".

Can I omitted those verbs?


thank you very much.

You can't omit である. It's like a more formal expression of です and you would probably never use it in conversation.

着ている means "John is wearing a blue sweater." Generally, ～ている of a verb is the progressive tense i.e. the -ing form. However, this isn't always the case. 太る is the verb "to become fat" but 太っている does not mean "getting fat" but simply "(is) fat". So, ジョンは太っている means "John is fat."

If that was confusing (and I'm sure it was) check out Tae Kim's explanation >here<. His entire grammar guide is really good so I would study it entirely.