noun which may take the genitive case particle 'no', na-adjective, noun
optional; voluntary; any; arbitrary
General use: something left to one's own choice, not compulsory, or freely selectable. Covers 'optional', 'voluntary', 'discretionary', and 'any' in the sense of 'any one you like'.
参加は任意です。
Participation is optional.
Please choose any number.
noun which may take the genitive case particle 'no', na-adjective, noun
Mathematics: an arbitrary element or value chosen without specific constraints.
任意の実数 x に対して、この不等式が成り立つ。
For any real number x, this inequality holds.