Below are some grammar points that are commonly found in formal writing, but not normally used when speaking.
～まい
editLet's not / Shouldn't. Negative volition or negative conjecture. Same as ～V(negative)ようにしよう or ~ないだろう
| Verb: godan type | (plain, present) + まい | 行くまい、歌うまい |
| Verb: all other types* | (negative stem) + まい | 忘れまい、できまい |
| i-Adjective | ～くはあるまい | 遠くあるまい、よくあるまい |
| na-Adjective | ～ではあるまい | きれいではあるまい、不便ではあるまい |
* Verb types other than that of the godan type most often have まい most often attached to the negative stem of the verb, but occasionally one sees まい attached to the plain form of these verbs also.