Jeg vil ikke give op.

Jeg is the subject form, like I in English. In Jeg vil ikke give op, the speaker is the one doing the action, so Danish uses jeg.

Use mig when it is an object, like me:

• Han ser mig. = He sees me.

Here, vil means want to.

So:

• Jeg vil ... = I want to ...

Danish vil can also sometimes be understood as will in certain contexts, but in everyday sentences like this one, it very often means want to rather than simple future.

In Danish main clauses, ikke usually comes after the finite verb. In this sentence, the finite verb is vil.

So the pattern is:

• Jeg (subject)
• vil (finite verb)
• ikke (not)
• give op (infinitive verb phrase)

That is why Danish says:

• Jeg vil ikke give op.

This is different from English word order, where not comes before give up, but after will/want:

• I do not want to give up.

Because after modal verbs like vil, Danish normally uses the infinitive without at.

So:

• Jeg vil give op. = I want to give up.

Compare:

• Jeg prøver at give op. = I am trying to give up.

After prøver, you need at. After vil, you do not.

Other common modal verbs that also take the bare infinitive include:

• kan = can
• skal = shall / have to
• må = may / must
• bør = should

Yes. Give op is a fixed verb expression meaning give up.

Even though it looks like give + op, you should learn it as a single expression, much like an English phrasal verb.

Examples:

• Han giver op. = He gives up.
• Vi gav ikke op. = We did not give up.

Because after vil, Danish uses the infinitive form of the verb.

The infinitive is:

• give

The present tense is:

• giver

So:

• Jeg giver op. = I give up / I am giving up.
• Jeg vil give op. = I want to give up.

Usually, op stays with give as part of the expression give op.

So:

• Jeg vil ikke give op. is correct.

In some Danish verb constructions, small particles can move depending on sentence structure, but for a learner, it is safest to treat give op as a set expression and keep the two together unless you see a clear example showing otherwise.

In a yes/no question, Danish usually puts the finite verb before the subject.

So:

• Vil jeg ikke give op?

That is the direct question form, though in real life this exact sentence may sound a bit unusual depending on context.

A more natural example:

• Vil du ikke give op? = Won’t you give up? / Don’t you want to give up?

The important grammar point is that vil moves in front of the subject in questions.

You change vil to a past form if needed, depending on meaning.

A common option is:

• Jeg ville ikke give op.

This can mean:

• I did not want to give up or sometimes
• I would not give up

So ville can cover more than one English idea, depending on context.

If you simply want I did not give up, that is different:

• Jeg gav ikke op.

It is neutral and completely natural in both speech and writing. It is not especially formal or especially casual.

You could also say more explicit versions, such as:

• Jeg ønsker ikke at give op. = I do not wish to give up.

But Jeg vil ikke give op is the most direct and everyday way to say it.

Jeg is often pronounced much more softly than learners expect. In careful speech, it may sound something like yai, but in everyday Danish it can be reduced further depending on region and speaking style.

A learner should be aware that:

• the spelling and the real pronunciation may feel quite different
• native speakers often pronounce common words very lightly

If you are focusing on grammar, just remember that the written form is jeg, even if the spoken form sounds less clear.

Yes, but that means something slightly different.

• give op = give up
• give op på noget/nogen = give up on something/someone

Examples:

• Jeg vil ikke give op. = I don’t want to give up.
• Jeg vil ikke give op på dig. = I don’t want to give up on you.

So the basic sentence is complete on its own, but på + noun/pronoun can be added when you mean give up on someone or something.