Grammar detail: まい

まい - negative volitional
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The negative volitional expresses the idea of wanting something not to happen, or being determined for something not to happen. It evokes the opposite of the normal volitional (which means 'let's ~' or 'shall we'), and even more strongly ('determined not to do'). In Japanese, it is formed by adding まい to the plain form of ごだん verbs, and the verb stem of いちだん verbs (although the plain form is also sometimes used).
For example:
る (see)
まい (determined not to see)
べる (eat)
べまい (determined not to eat)
Note that べるまい is also commonly seen
ある (exist) あるまい (could not possibly exist)
No ... there couldn't possibly be such a thing.
The まい form can also be attached to the ます form of a verb for additional formality.
For irregular verbs する and くる, various forms are seen in use, but すまい and こまい are most common.
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See also:
  • verb volitional form - let's ~, shall we ~
  • かろう - negative volitional

Kanji used in this grammar

ケン   み to see   みえる to be seen; to appear   みせる to show   
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ショク   ジキ    food   たべる to eat   く to eat   
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