得ない|えない

1. 1Something cannot possibly be the case or happen (especially in the set phrase あり得ない).Ex. 1
2. 2It is impossible to do the action; the action cannot be carried out or even conceived.Ex. 2

A formal, somewhat written expression of impossibility, common in essays, reports and argument. The set phrase あり得ない is also very common in everyday speech, including as an exclamation. Unlike がたい or かねる, which mean "difficult" or "unable due to circumstances", 得ない is a flat statement that something is logically or practically impossible.

• 得るN2得る is the affirmative counterpart of 得ない and has the opposite meaning, "can" or "be possible," so the two are not interchangeable. Both attach to the ます-stem, but 得る is read うる or える, while 得ない is read only えない and never うない.
• べくもないN1べくもない follows the dictionary form, mostly with a few verbs such as 望む, 知る, and 疑う, and means something is out of the question given the situation, whereas 得ない attaches to the ます-stem and flatly states that something is objectively impossible. Both lean formal, though あり得ない is also common in speech.
• かねるN2かねる also attaches to the ます-stem, but it marks something as inappropriate to do because of one's position, rules, or propriety rather than impossible in principle or beyond one's ability, and it is typically used for polite, indirect refusals; it can also express hesitation or feeling unable to bear something. The two are generally not interchangeable.
• かねないN2かねない also takes the ます-stem and contains ない, yet means the opposite: something bad could well happen, carrying a note of concern or warning, while 得ない asserts that something is impossible. They are not interchangeable, and かねない is also common in everyday warnings.
• がたいN3がたい also takes the ます-stem and means "hard to" or "almost impossible to," usually describing psychological difficulty in accepting something (信じがたい) but sometimes objective difficulty. 得ない asserts outright impossibility and is more absolute, so the two are generally not interchangeable.
• にたえる / にたえないN1得ない takes the ます-stem and asserts objective impossibility, whereas にたえない follows the dictionary form or a noun and means "unbearable" or "cannot bear to," or "overwhelmed with" after words like 感謝, and にたえる means "can withstand" or "be worthy of." The two are not interchangeable.

得る is the affirmative, meaning "can happen / is possible". べくもない is a more literary "cannot even hope to". かねる means "unable to (because of circumstances)" and is often a polite refusal, while かねない means "might well (something bad)". がたい means "hard to" rather than strictly impossible, and にたえない means "unbearable to ~" or "deeply (grateful etc.)", not impossibility.