# Do 以上 and 以下 include the number preceding them?

I was having a discussion with a colleague and we couldn't recall how they both worked. Does 一人以上 mean a) 1 or more persons or b) more than one person?

• I see good answers below. These are among the words that are often used incorrectly by people who don't understand basic mathematics. Other than these, `楕円` 'ellipse' is often used incorrectly as 'distorted circle', and `比例` 'proportional' as 'monotone increasing', and `反比例` 'inverse proportinal' as 'monotone decreasing' by these kinds of people. It's a bad habit. Especially for `以上`, `以下`, `比例`, and `反比例`, they should have learned them at elementary school, but somehow they forget it. – user458 Jul 7 '11 at 2:33
• @sawa: That’s life, and that’s language. Should the law forbid mathematically incorrect use of mathematical terms? :) – Tsuyoshi Ito Jul 7 '11 at 14:29
• @Tsuyoshi_Ito Thanks for the comment. Language change by convention, but there are obviously wrong usages. Especially for words that were created/stated by particular (group of) people like techincal terms or proper nouns, it is them who decide what is correct. Derek's comment on your answer is suggestive. In legal documents, it may matter. – user458 Jul 7 '11 at 15:25
• @sawa: I will stop commenting about this point here, but I do not think that the matter is as simple as your comment: “Especially for words that […], it is them who decide what is correct.” – Tsuyoshi Ito Jul 7 '11 at 19:37
• If you want to be more precise, you can use 「かそれ以上」, like「3人かそれ以上の人」。 – Tomei Ningen Dec 7 '12 at 3:32

According to the Wikipedia article on these two, 以下 and 以上 include the number that precedes them.

５０以上 => 50 or more

５０以下 => 50 or less

If you want to exclude the number on the upper end (instead of 以下) use 未満(みまん).

１０００円未満 (less than 1,000 yen, not including 1,000)

I had a few different discussions (and taking Ito-san's point below as well) about this - 超 seems to be used (?) but I've never really heard it. In this case we would probably go back to standard grammar using a verb instead:

１０００円を超える（こえる)

If there was really a need to exclude a certain number in the case of 以上, you could always add 1 to it -- e.g.

１００１円以上

Although that seems strange too. Maybe there's not much of a use for that kind of term?

• I have never seen “more than 1000 yen” stated as “1000円超過,” and that expression does not appear in the Wikipedia article which you linked. I have seen “1000円超 (read as せんえんちょう)” and “1000円を超過する.” – Tsuyoshi Ito Jul 6 '11 at 5:13
• Ito-san, Believe you're right - might have been mis-reading the Wikipedia article. Updated my answer. – makdad Jul 6 '11 at 12:41

As makdad and Axioplase stated in their answers, the “correct” usage is that X以上 and X以下 (where X is a number) include X. However, the “incorrect” usage with X excluded is not rare, and therefore it is better to be aware of this possibility, too. For example, when talking about a ski lift, some people may well say:

このリフトには一人以上乗ることはできません。 This lift cannot carry one or more persons. (What?!)

when they really mean “This lift cannot carry more than one person.”

• Are you sure this example isn't a loophole left in case of an accident and lawsuit? Suppose the lift comes apart and falls, injuring or killing the occupant. They could point to the capacity notice and say, "Well, we did say it couldn't carry one or more persons." ;) – Derek Schaab Jul 7 '11 at 14:14

I think 以上 and 以下 are inclusive above and below. 超 and 未満 are exclusive.