As I always make mistake with ㅔ and ㅐ, I always wondered why we use 겠 and not 갰, like in 알겠습니다.

Also, if there is any heuristic for ㅔ and ㅐ, please let me know.

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    I don't think an etymology is known, but "갰" doesn't appear in Standard Korean in any occasion. – Ignatius Oct 23 '19 at 0:51
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    Note that ㅔ and ㅐ are also different sounds in strictly standard Korean, and they are still quite different outside the Seoul / Gyeonggi-do areas. – Michaelyus Oct 23 '19 at 10:12
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    갰 is used in 갰다, past tense for 개다 - to fold. – Jihyung Kang Oct 23 '19 at 12:38
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    And though ㅔ and ㅐ should sound differently, even native Koreans can't tell differences between these two in everyday conversations. (They do know how to pronounce them differently, they just don't because it's a bit tedious) They are strictly differentiated in written languages, though; 네 means "your", and 내 means "my". – Jihyung Kang Oct 23 '19 at 12:43
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    It has been said that -겠- came from the abbreviation for -게 ᄒᆞ엿- (reference). – Klmo Oct 28 '19 at 11:10

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