If the japanese ranks follow the japanese numbers, then why not ichidan as one?
jwaytogo: Just to clarify, 初段 means initial dan/first dan/primary dan, while 一段 would just mean one dan. Even usage in english, we often say someone is "first dan", but I feel "three dan" is more common in daily usage than "third dan", although not unheard of. Although in common english usage, "one dan" is also used. I am assuming this is just convention. Languages usually place special emphasis on the first few numbered placings. Like in english, we say "first, second, third" before moving onto a more structured numbering by adding a "-th" suffix, "fourth, fifth, sixth" etc. Also, I am not sure if it is possible to write "third" in japanese kanji with one character, while it is possible to write "first/initial" by using 初. Maybe it is just practicality, "first kyu" is easy enough to say, but when it gets to "thirtieth kyu". most people would prefer to just say "thirty kyu" for simplicity's sake. Just my two cents worth of observations. Would like to be corrected if wrong.
The dan ranks in Japan are expressed using cardinal numbers rather than ordinal numbers. Using cardinal numbers fits well with translating 段 x (dan) a step in a progression of steps such as a staircase. 初 x means new, initial, and interestingly enough inexperienced or green. 第 x is used to convert cardinal numbers to ordinals: 三 (three) becomes 第三 (third).
Now we need someone who actually knows Japanese to comment. I am not even a tyro in the language.