sorry, a year late, but just in case it helps others. the proper form is "he aims to live FOR a long time" or "he aims to live a long life". there are lots of examples like "love you long time" in local dialects or street lingo, but its not common enough to be grammatically accepted yet.
I don't think that's true. While "live for a long time" sounds slightly more correct than "live a long time", Google's n-gram viewer shows "live a long time" consistently ahead of "live for a long time" for the last 200 years. In recent books it's twice as popular overall - in recent American books even three times as popular. (In recent British books it's only 50 % more popular.)
You can "live for 90 years", a long period of time; or you can "live 90 years" - every one of them. "Live for a long time" is clearly correct by analogy to "live for 90 years". But "live a long time" is just as correct by analogy to "live an exciting life" (or even the more far-fetched "live an exciting time").
Thinking about it this way, it appears to me that the following choices are more appropriate than the opposite ones:
- She had lived a long time, and now seemed as good a time as any to go on with the next step. She closed here eyes and fell into a peaceful sleep.
- The average subject continued to live for a long time after the injection.
Someone "aiming" to live [for] a long time can fit the first or the second pattern depending on whether they plan to live a long and fulfilled life or to get into the Guinness Book of Records while on life support.
Naar ... streven (strive for ...) cannot be called a separable verb because the infinitive is never written in a single word.
When you say "Hij streeft naar ..." ("He strives for ..."), what follows must be a noun, or something sufficiently similar to a noun. In English, the gerund does the job sufficiently well so that you can use it, even though it's not ideal: "He strives for living long".
In Dutch, the equivalent of the gerund, i.e. the verb form that can function as a noun, is the infinitive. But it cannot be used in this way unless you really treat it as a noun. The infinitive leven happens to be identical with the Dutch word for life. But treating leven as a noun also means adjusting the word order and conjugating the adjective (not adverb). And usually it requires an article. "Hij streeft naar een lang leven."
What we really need is some glue that allows us to use lang te leven (to live long) with a verb that really requires naar [noun] (for [noun]). The solution is ernaar, which means roughly for that. (It's related to the English word therefore, but therefore has changed its meaning a lot.)
- Hij streeft / ernaar / om lang te leven.
- He strives / for that / to live long.
Ernaar is needed as the glue or adapter that connects the verb naar iets streven (strive for something) with the phrase [om] lang te leven. Without it they don't fit together, as in the case of a wrong case / wrong preposition. English is more liberal in these situations and generally doesn't require such glue. (In this case, in English you can just drop the for.)
In an earlier sentence where "streven ernaar" was present, someone in the comments asked why "om" was not part of the correct answer, and was then told that you don't use "om" when you use "ernaar." Why is that not the case here? Do you just not use "om" when you're talking in plural?
What you are reporting from another discussion doesn't make sense to me. I don't think om has anything to do with ernaar, or with singular/plural, for that matter.
As a first approximation, te corresponds to to and om te corresponds to archaic for to and modern in order to. So it's used when indicating a goal. But it's used much more generally than in order to, in much the same way that for to was used much more generally. (Example: "My destiny is for to dy a shamefull deth, I trowe.")
Since my native German works more like English in this respect, it's confusing for me, too. But maybe this criterion works: In situations when in English there is an alternative construction with for and a gerund, then I would expect om te to be used in Dutch. In the present case there is one: "I strive for living long."