So does 'aan' mean 'on' as well as 'to'? If 'op' also means 'on' then can the sentence be 'hij heeft geen jas op'?
To answer your question; yes, 'aan' has many translations in English, but that doesn't mean that they're interchangeable. In this case, 'aan' belongs to the verb, 'aanhebben', which means 'to wear' (lit. 'to have [piece of clothing] on'). So, the context is important to know what 'aan' (or 'op') means. If it's at the end of the sentence, it'll belong to the verb.
"aan" can be translated to different things in English, as does "op". In most cases, if not all, though "aan" and "op" are not interchangeable.
In this case it can only be "aan", "op" would only be suitable if you put a piece of clothing "on top of" your body. Some examples.
"He puts on a coat" - "Hij doet een jas aan" / "Hij trekt een jas aan"
"He puts on his trousers" - "Hij doet zijn broek aan" / "Hij trekt zijn broek aan"
"He puts on a hat" - "Hij zet een hoed op"
"He puts on his glasses" - "Hij zet zijn bril op"
I also put, "He does not have on a coat." It was marked wrong. I have been taught that one doesn't end an English sentence with a preposition...? (12-31-2017)
As explained elsewhere in this topic this is an example where "have ... on" is not the same verb as "have", and "on" is not introducing an indirect object.
All the same, "have on a coat" could be correct in some versions of english but sounds awfully old fashioned in british english, and still the "on" is modifying the verb, so isnt working as a preposition. Nothing is "on the coat"!
We also have verbs that look separable but are not. So "put up" in "put up with" or "endure" is rarely if ever split except in an infamous churchill quote "(this is) something up with which i will not put". That version is and certainly sounds pedantic and alien. The test i would use is "does the preposition really work like a preposition or not?" It does in "have a jacket on" only if you add a missing indirect object "have a jacket on (his shoulders)". But then it is no longer "wear" but just "have" again! "Put up" in the sense of erect is also like a separable verb, so i believe that "i put up a tent" and "i put a tent up" are both correct. Again, nothing is "up the tent" so "up" isnt working as a preposition. Dutch is rather more regular than english i think!
Your form is probably more widespread in America, and should absolutely be an accepted alternative. However, it is as well to remember the (probably misattributed) Winston Churchill quote, to a copy editor who attempted to correct his copy: "This is the sort of arrant nonsense up with which I will not put!".
Before (and after) John Dryden (apparently) introduced the "no prepositions at the end" rule ex nihilo in 1672 English quite happily put prepositions at the end, sometimes more than one at a time. ("What are you up to?") But then, unlike Latin and derivative Romance languages, English favours phrasal verbs - so it is no surprise that the natural word order should give us terminal prepositions. This is clearer in question forms. You would never, for example, say "May I in come?" but "May I come in?" That's natural English, and to try to circumvent it with something like "May I enter?" is, I contend, Churchill's "arrant nonsense".
No, you're mixing up Hij heeft geen jas aan and Hij draagt geen jas
- You wear a coat - Je draagt een jas, or
- You have a coat on - Je hebt een jas aan
If one were to remove the aan, then yes, "he has no coat" would be acceptable. However, the verb we're looking at is not hebben, but instead aanhebben, a seperable verb (which means the root infinitive, hebben, has a preposition at the start, in this case aan, which goes to the end when the verb is used in the present tense)
Hebben and aanhebben are completely different verbs (just like to have and to have on are in English), but, unlike most seperable verbs in Dutch, this corresponds directly to English, making this easier than most.
No, that would mean "he is not wearing any coats", which would imply that he has multiple coats but is wearing none.
In English it is incorrect to end a sentence with a preposition. “He does not have on a coat” IS correct
In UK English grammar, it is incorrect to end a sentence with a preposition. My answer: "he does not have on a coat" is grammatically correct and retains the meaning absolutely - so should be accepted