Is "元気" a grammatical sentence in modern Japanese?


From what I remember reading, a sentence in Japanese must either end with an
adjective, a copula or a verb, if we exclude sentence ending particles and
inflections. This being the case, I'm under the belief that "元気" by itself
does not constitute a grammatically correct sentence in modern Japanese. Is
this correct?

Furthermore, I'd like to know how a Japanese sentence is rigorously defined
and what components are necessary.




Yes, I believe it's a Japanese sentence (sometimes called a minor sentence or
a [sentence word](https://en.wikipedia.org/wiki/Sentence_word)).

Looks like many English speakers were [taught at
school](https://japanese.stackexchange.com/a/48864/5010) that a sentence
_must_ contain a predicate (a verb or a copula). However, as a native Japanese
speaker, I have never heard such a rule from Japanese teachers in schools in
Japan. Things like `元気。`, `はい。`, `おはよう。` or `わ！` are always perfectly
grammatical Japanese sentences to me. Simply, any valid expressions delimited
by periods (or question/exclamation marks) are grammatically sentences. Some
consider these "incomplete" sentences, but they are not even incomplete to me;
there is no "full version" of こんにちは, for example.

If you look at the [Wikipedia article about
sentence](https://en.wikipedia.org/wiki/Sentence_\(linguistics\)), you can see
many linguists think a sentence does not have to contain a predicate.
Something like "Mary!" or "Wow!" are sentences to them.




Yes, I believe it's a Japanese sentence (sometimes called a minor sentence or
a [sentence word](https://en.wikipedia.org/wiki/Sentence_word)).

Looks like many English speakers were [taught at
school](https://japanese.stackexchange.com/a/48864/5010) that a sentence
_must_ contain a predicate (a verb or a copula). However, as a native Japanese
speaker, I have never heard such a rule from Japanese teachers in schools in
Japan. Things like `元気。`, `はい。`, `おはよう。` or `わ！` are always perfectly
grammatical Japanese sentences to me. Simply, any valid expressions delimited
by periods (or question/exclamation marks) are grammatically sentences. Some
consider these "incomplete" sentences, but they are not even incomplete to me;
there is no "full version" of こんにちは, for example.

If you look at the [Wikipedia article about
sentence](https://en.wikipedia.org/wiki/Sentence_\(linguistics\)), you can see
many linguists think a sentence does not have to contain a predicate.
Something like "Mary!" or "Wow!" are sentences to them.

