– “ijou” – X or more
– “ika” – X or less
– “miman” – less than (but not including) X
Interestingly, there is no commonly used kanji expression for “more than (but not including)”. The formal opposite of “miman” is “chou”, using the kanji for “koeru”, to surpass. However, most Japanese people themselves don’t know this word in this meaning, and it is not in common usage. More common are the simple phrases “X yori ookii” (bigger than X) and “X yori chiisai” (smaller than X).
In Japanese, “ijou” and “ika” are the most commonly used. In English, however, “more than” and “less than” are more common. And this is where the confusion in translating comes in. Translators are taught at a very early stage to always distinguish these expressions carefully, and translate accordingly. But mistakes happen, and in some cases can be quite serious.
For example, take an instruction manual that says “Soushin botan wo 2kai ijou osanaide kudasai” (transliterally, “Submit button (object marker) 2 times or more don’t_press please”).
This could be easily (though mistakenly) translated into English as “Do not press the submit button more than two times”. In this sentence, of course, pressing it twice is now OK!