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On the temperature in eastern Russia:

気温がいつもの年より10℃以上低い-50℃以上になっている所がたくさんあります。
There are many places that have reached less than -50℃, which is 10℃ lower than usual years.

Firstly, I was fairly confident in my translation, but I read an English article that said the average temperature in a normal year was -50℃, whereas my translation suggests that -40℃ is the usual temperature, so now I'm not so sure.

My main question is about the use of 以上 and 以下 with negative numbers. This sentence is opposite to my expectations. My usual understanding would be that -50以上 means 'not less than -50' i.e it could be -40, -30 etc. But from the context I must assume that it means temperatures colder than -50.

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I think your understanding is perfectly correct. Mathematically "-50℃以上" must mean -40, -30, 10, etc., but from the context I also think it refers to temperatures colder than or equal to -50℃. "-50℃以下" should have been the correct wording. Perhaps the person who wrote this is not good at math. Rest assured there is no strange Japanese rule regarding negative numbers and the usage of 以上/以下.

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