任意

1. Origins, structure, and basic meaning

• Structure: The adjectival noun 任意 (にんい) marks something as freely chosen rather than compulsory.
• Basic usage: 任意の数字 means any selected number, while 参加は任意 says participation is optional.

2. Common pitfalls and similar expressions

• Free choice and optional status
  • Arbitrary here does not necessarily mean careless or random; it indicates that a choice is left open.