In English an article - either definite or indefinite - is compulsory before countable objects.
On the other hand Hungarian, does not have these strict rules. Hungarian is very flexible. That is especially true for the word order and leaving out articles.
So both "Ez nem egy nagy óra" and "Ez nem nagy óra" are correct.
And I could continue: Ez az óra nem nagy. Nem nagy ez az óra. * Nem ez a nagy óra.
These are all valid, although playing with the word order changes the meaning of the sentence a bit.
What a good question! And this sentence is another one where you would not need the "egy", although it would be allowed. It is generally true, not just in negation. I am a teacher. Tanár vagyok. I am not a teacher. Nem vagyok tanár. You could include the "egy", and it would slightly alter the meaning.
Maybe you can use Spanish as a reference when it comes to the use of the indefinite article. Spanish is very close to English (from a Hungarian standpoint) but its usage of "un" is different. It actually very much reminds me of the Hungarian pattern. For one thing, in both languages, the indefinite article also means "one". Not so in English. Of course there are many more languages like that, this is just an example.
You just run into another group of exceptions. I don't know about Spanish, but in Hungarian you never use "egy" when you speak about your own profession. I am a doctor = Orvos vagyok. I am not a doctor = Nem vagyok orvos. You don't say "Egy orvos vagyok" or "Nem egy orvos vagyok". Consequently, you can't use "egy" with "Tanár vagyok".
Except when you can. :) Én csak egy orvos vagyok, de ... Én csak egy (egyszerű) tanár vagyok... Etc. It depends on context.
But I think your rule stands for anybody's profession, not just your own, doesn't it? Én tanár vagyok, te tanár vagy, ő tanár.
And yes, the above matches the Spanish usage, as far as I know.
Yes, it is context-dependant. But just to clear things up, at this level I was talking specifically about these simple sentences, like your sentence above, where "egy" would sound very out of place. Now I don't know if there's an actual rule for this, but if someone asked your profession, answering with "Egy tanár vagyok" would sound off and something -in my experience- a foreigner would typically say. In second and third person, I think it's more acceptable. But correct me if I'm wrong, grammar's not my strong suit. :D
I'm not a native speaker, so I could be wrong.
It seems to me like "nem" negates something. It negates what comes right after it. So saying "Ez nem egy nagy óra" is saying "What is it that this thing is not? It is not a big clock."
Whereas "Ez nem nagy óra" is more along the lines of "Not big is what this clock is."
But I don't think the difference is that big. This is just being pedantic.
Hey I guessed great and it marked me wrong but when I scrolled over the word it said that was a possibility. This is not a great clock lol. Like it could work better. I didn't know it had other meanings besides great because I've mostly heard it describing family members like nagy papa or nagy bacsi.
"Ez óra nem nagy." doesn't sound good. One could argue that it actually preserves archaic (older than Shakespeare) grammar but as of now, we may call it wrong. "Ez óra" can mean "this is a clock" on its own but it cannot mean "this clock" as one phrase. That should be "ez az óra" (which, as you might have guessed, can also mean "this is the clock" on its own).
Also, syntactically, "ez az óra nem nagy" is clearly not the same as "ez nem (egy) nagy óra". The same stands for "This is not a big clock" and "This clock isn't big". You can argue these sentences have a very similar meaning which makes them interchangable in 95% of all cases - but we are here to teach syntax. "this" is a demonstrative pronoun here, not a demonstrative adjective, also you can see the lack of indefinite article is acceptable in the Hungarian variant.
You can already see these sentences aren't just permutations of each other (as "az" showed up in one of them) but let's take it a bit further. "Ezek az órák nagyok" vs "Ezek nagy órák" - as you can see, pluralization of "nagy" changed because in the former case, it's predicative (it belongs to the copula verb) and in the latter case, it's attributive (it belongs to the noun).