Understanding Negative of Verbs

I understand the negative verbs to be the negative of a positive, eg. run → to not run
my confusion is over translate of verbs such as this sentance (From Tae Kims guide):
先生が学校に行ったか 教えない
which translates as:
“Won’t you inform me whether teacher went to school?”
my confusion is over the “wont you” part of the sentance, stemming from 「教えない」. Can someone please explain to me as if i am an infant why this translates to “wont you tell me” instead of “not to tell” / “dont tell me”. And please explain how to understand this in sentences as it consistently slips me up.

Thanks for any help.

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(post deleted by author)

No worries! Without actually hearing the sentence contextually, these sentences can be difficult to read sometimes (especially in the beginning). Japanese is a very contextual language. If we think of this example using English with your translation:

Don’t tell me whether the teacher went to school?
It doesn’t really make sense in English either, right? It would be a strange thing to say.

Now…
Won’t you tell me whether the teacher went to school?
It makes sense.

Make sure you’re reading these questions with a higher pitch at the end so you register it as an informal question.

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I’m understanding it differently but I’m also fairly a n00b when it comes to learning Japanese. The point being the か making a question within the sentence. So I can’t quite figure out why the whole thing is interpreted as a question sentence and not as a statement with an embedded question that gets answered right away.

先生が学校に行ったか
Did the teacher go to school?
教えない
(I) won’t tell

=> I won’t tell, if the teacher went to school (or not)

this is how I’d read it

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right, that makes sense, using a higher pitch when reading makes it much more obvious that it is a question and allows you to pick the right translation within the context, thank you for the help!

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This grammar point in particular may help further shed some light on your troubles, in addition to what the above responses have already laid out~

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先生が学校に行ったか → Did the teacher go to school?
教えない? → Won’t you tell me?

You’re making the same mistake OP is making. You’re reading the second part as a statement and not a question.

Just to add a bit more… let’s take a super easy sentence and apply the same reasoning.
寒くない。 → It’s not cold.
寒くない? → Isn’t it cold?

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I think your statement makes it even clearer. the か comes after いった, marking this part of the sentence as a question, while the negation in 教えない marks it as a soft request, as in the above linked grammar point …ませんか.

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Just double checked on tae kim the sentence, and thought i’d attach how it looks there. not sure if the lack of question mark was also throwing you off, but i noticed you didn’t have it in your OP so just wanted to make sure.

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I understand now, thanks

Just for further clarification: would my interpretation have been invalid even without the question mark based on what Chimmsen said?

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I think depending on context, your interpretation could be possible (probably less likely though when you think about the meaning). Maybe a student is being super cheeky to their friend or something though.

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