Syg is used as an adjective here. Those do not get a noun treatment, but have to keep the article separate: en syge, den syge, de syge. Remember studerende? It's the same here.
But then again the Danske Ordbog tells us that syge can also be used as a base noun, so your sentence would be good as well.
Could this be translated as "the physicians treat the sick" instead of "the doctors ..."? I had decided to use "læg" = physician, "doktor" = doctor, and treat them as synonyms. Am I wrong?
I am a doctor (of mathematics), but you would not want me to treat the sick.
A læge is a physician (who is allowed to touch people and give them medicine). A doktor is someone who has studied and earned a doctorate. So, yes, "physician" would be more appropriate here, but English mostly doesn't care and calls them all "doctor".
I wonder when it will be accepted; I have reported the correct answer as a correct one on several questions and even started a thread on it, but it still seems to be accepted nowhere.
I don't remember having any of the sentences I suggested in this course be accepted (and I've been around for more than two years), so I'm just assuming that no one is taking care of it anymore.
"The sick" is plural, if it were singular there would be something after it in English ("the sick one" or "the sick person/thing")
As in "Robin Hood steals from the rich (ones) and gives to the poor (ones)."
"Treat the sick" means treat the sick people.
If you mean "treat the illness," you have to say just that or treat the sickness/treat the disease.
How to make difference between "lægerne" and "lærerne" ?? Maybe I am deft :D
The 'ge' and 're' have slightly different sounds. Phonetically: [ˈlεːjə] is læge and [ˈlεːʌ] is lære.
A tip is to listen to the sound/length of the vowel. It might be that the audio here won't let you hear the difference - but in real life, it's not as hard.