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In mails and documents I see the phrases「下記に表します」、「以下に表します」or 「下記の件。。。」、「以下の件。。。」.

I know they're both saying "the following (see below, etc)", but are there cases when you should use one over the other or are they pretty much always interchangeable?

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Let me start by saying that 下記{かき}can only be used with the meaning of "below", "hereafter", whereas 以下{いか}has many other meanings, most notably "less than", "not more than", "not exceeding (some amount)".

When talking about text that will follow the current sentence, both can be used. There is however a subtle difference, that shouldn't matter much outside of formal contexts:

  • When using 以下, the following text should be on the same line / in the same paragraph, i.e. follow immediately without changes in appearance.
  • Using 下記 means that the follow-up text will occupy a whole text unit, i.e. a full paragraph, or maybe a bullet-point list. It can also refer to some bibliography item or attached document.
  • Please explain within the current context and maybe I just don't know about those "rules", but then it would seem like the 100+ Japanese staff I work with don't either... – Y12K Apr 10 '17 at 5:52
  • Sorry what is out of context? As I pointed out, it is a quite formal rule, and I am not surprised that your colleagues would not know (I had to look for it myself). If you look for example here: ameblo.jp/kyousituower/entry-11294344228.html You will see that 下記 should refer to a distinct unit of text, a 記. – Urukann Apr 10 '17 at 5:57
  • sorry I was a bit hasty, I do know that「以下」has other meanings. So was only looking for a an explanation with the context of, "below" or "the following". So most Japanese people wouldn't even consider the difference and would just use them interchangeably even if 'formally' it should be used in these ways? – Y12K Apr 10 '17 at 6:01
  • Yes, that is my understanding: most people do not really make a difference, but it could be important when writing a research paper for example, where 下記 would probably refer to some specific item. – Urukann Apr 10 '17 at 6:15
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In this context, 以下 just means "(something) below" whereas 下記 is "(something) written below". You can say 以下に述べます, 以下に記します or 以下に記載, but 下記に述べます, 下記に記します or 下記に記載 would look like a weird 重言 to me. In reality you may occasionally see them, though.

以下 and 下記 are interchangeable in sentences such as 以下をご覧ください/下記をご覧ください, 以下の件/下記の件, 以下の通りです/下記の通りです and 以下参照/下記参照.

In vertical writings 下記 becomes 左記.

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