"It is not nine o'clock now."
Because when you're using the negative form, instead of the positive desu, you need dewaarimasen. No, I'm not entirely sure of the 'why' of that, but that does seem to be the pattern. arimasu seems to be 'have' so maybe the dewa is used with that to translate if not transliterate to is not.
I agree that it is tedious and unnecessary in the beginner's courses, but the split is not arbitrary. あり (adverbial form of the verb ある - exist) + ませ (irrealis form of auxiliary verb ます - to express politeness) + ん (sound reduction of auxiliary verb ぬ - to express negative)
I stand corrected. Thank you for generously sharing your knowledge. It's kind of too bad that the lesson structure doesn't really explain that. Having no insight into the split makes it even more annoying to have to peck at those three bricks so. many. times. Of course, knowing the pleasure of "ja," I also begrudge the insistence on "de wa," so I might just be kind of hard to please. :)
in casual conversations the では is usually contracted to じゃ so じゃない is more common as as the less formal version. ではない and even じゃありません are possible but to my knowledge they are rarely used.
じゃないです is also possible, and more common than ではない or じゃありません. In terms of formality it's somewhere in between じゃない and ではありません.
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Strictly speaking no because this is not a correct form. It should be just ではない in plain form and ではありません in polite form (and noting that there are other even more polite forms).
However I have read from the internet that more and more Japanese start to accept this form, because it sounds softer than ではありません and is not rude like ではない. Personally I do not recommend to use it before we have built up a solid habit to apply the normal polite form and plain form which are needed for understanding more complicated sentences in the future.