Kanji for ordinal numbers

Question

I am beginning to study kanji and while reading a wiki I noticed only the ordinal numbers first (初), second (乙), and third (丙) are listed. Which brings me to ask whether there are symbols for fourth, fifth, and so on or if these are the only ones available; I am not knowledgeable on ordinal counting in Japanese.

Answer 1

初{はつ} is actually used in a completely different way from 乙{おつ}, 丙{へい}, etc:

初

初 means first, but only first in the temporal sense of a first occurence. Therefore, it isn't used as an ordinal to number/rank items in a list.

Instead, it's used as a part of various compound words, where it signifies the 1st occurence of that thing; often as a prefix, such as in 初詣{はつもうで}, 初耳{はつみみ}, 初恋{はつこい}, 初雪{はつゆき}; or as a suffix, such as in 業界初{ぎょうかいはつ}; or even just by itself, as in ”初{はつ}です”—another way to say ”初{はじ}めてです”.

Counting in Japanese

This is large topic due to the existence of many different kinds of counter suffices, depending on the thing being counted (e.g., 一個, 一本, 一冊, 一人, 一名, 一匹). Trying to list them all would go way beyond the scope of this answer, but one of the most generic way to count things involves using the 目{め} suffix: 一つ目, 二つ目, 三つ目, ...

Among these many ways to count things in Japanese, there exists a classic Chinese system that uses a separate set of kanji as its ordinals:

十干: The Ten Heavenly Stems

乙{おつ} and 丙{へい} are part of the Ten Heavenly Stems, originating in Shang Dynasty China, called 十干{じっかん} in Japanese.

They are rarely used in day-to-day Japanese; mainly reserved for usage as ordinals in legal documents. Note that 甲{こう} rather than 初 belongs in this list as the first ordinal:

1. 甲{こう}
2. 乙{おつ}
3. 丙{へい}
4. 丁{てい}
5. 戊{ぼ}
6. 己{き}
7. 庚{こう}
8. 辛{しん}
9. 壬{じん}
10. 癸{き}

They have calendar, fortune-telling and angle-related interpretations too, as well as (rarely used) 訓読み readings. More information about that can be found in the same Wikipedia article.