Az idegen nem vendég.

Hungarian has two forms of the definite article:

• a before a consonant
• az before a vowel

Because idegen begins with the vowel i, the correct form is az idegen.

Compare:

• a vendég = the guest
• az idegen = the stranger / the foreigner

Because Hungarian often leaves out the verb to be in the present tense, third person, when the predicate is a noun or an adjective.

So:

• Az idegen nem vendég. = The stranger is not a guest.

Literally, it looks more like:

• The stranger not guest.

This is completely normal Hungarian.

But the verb appears in other persons and tenses:

• Idegen vagyok. = I am a stranger.
• Az idegen vendég volt. = The stranger was a guest.

Idegen can mean several related things, depending on context:

• stranger
• foreigner
• unknown person
• more generally, someone/something foreign or unfamiliar

In this sentence, it is functioning as a noun: the stranger / the foreigner / the outsider.

It can also be an adjective in other sentences, for example:

• idegen ember = a strange / unknown person
• idegen nyelv = a foreign language

So a learner often has to rely on context to decide which English word fits best.

Because vendég is a predicate noun here, and in this kind of sentence Hungarian normally does not use an article.

So:

• Az idegen nem vendég. = The stranger is not a guest.

This means the person does not belong to the category guest.

If you add the definite article, the meaning changes:

• Az idegen nem a vendég. = The stranger is not the guest.

That version contrasts the stranger with some specific guest.

This is a very important distinction.

• nem vendég = not a guest, not in the role/category of guest
• nem a vendég = not the guest, not that specific person

So:

• Az idegen nem vendég.
  The stranger is not a guest.

• Az idegen nem a vendég.
  The stranger is not the guest.

English speakers often want to add an article automatically, but in Hungarian that changes the meaning.

Nem is the basic Hungarian word for not.

In this sentence, it negates the predicate:

• vendég = guest
• nem vendég = not a guest

In neutral sentences, nem usually comes directly before the part being negated.

So here the structure is:

• Az idegen = the stranger
• nem vendég = is not a guest

The word order here is the most neutral, straightforward one:

• Az idegen = topic / what we are talking about
• nem vendég = comment about it

So Az idegen nem vendég is the natural default order.

Hungarian word order is flexible, though, and changing it changes the emphasis. For example:

• Nem vendég az idegen.

This is still grammatical, but it sounds more emphatic or contrastive, something like:

• The stranger is not a guest.

So the original sentence is the most neutral version.

Because both nouns are in their basic form here.

• idegen is the subject
• vendég is the predicate noun

In Hungarian, the subject is normally unmarked, and predicate nouns in sentences like this are also unmarked.

So you do not need any extra ending to say:

• X is Y
• X is not Y

That is why both words appear in their dictionary form.

In ordinary usage, az idegen is grammatically definite, so it most naturally means the stranger or the foreigner.

However, Hungarian sometimes uses the definite article in broader, more general statements too, especially in proverb-like or class-type statements. So depending on context, it can feel more general than English the stranger sometimes does.

If you want to clearly say a stranger, Hungarian would usually use:

• egy idegen

So:

• Egy idegen nem vendég. = A stranger is not a guest.

A simple learner-friendly guide is:

• az — short, with z pronounced
• idegen — I-de-gen
• nem — like nem with a short e
• vendég — VEN-dayg, with a long é

A few useful pronunciation points:

• Hungarian stress is always on the first syllable of each word.
• é is a long vowel.
• g is always hard, as in go.

So the stress pattern is:

• AZ I-de-gen NEM VEN-dég

In the plural, both nouns become plural:

• Az idegenek nem vendégek. = The strangers are not guests.

Notice that Hungarian still does not use the verb are here in the present tense, third person, because the same rule applies.

Singular:

• Az idegen nem vendég.

Plural:

• Az idegenek nem vendégek.

Then the verb to be usually appears.

Examples:

• Idegen vagyok. = I am a stranger.
• Idegen vagy. = You are a stranger.
• Az idegen vendég volt. = The stranger was a guest.
• Az idegen nem volt vendég. = The stranger was not a guest.

So the missing is in the original sentence is not because Hungarian never uses to be. It is specifically because this is a present-tense, third-person, nominal sentence.

Yes. It is short, correct, and natural.

It has a slightly firm, categorical feel because it is a simple classification statement:

• Az idegen = the stranger / outsider
• nem vendég = is not a guest

So it sounds like a direct statement of status or role, not a description of an action.