By accident means without meaning to. Nobody planned it and it happened anyway.
It follows the verb and it is the everyday opposite of on purpose. There is a second sense meaning by chance rather than by mistake, so discovering something by accident means stumbling on it, and a great many scientific discoveries are described that way. By mistake is close but not identical, since a mistake implies you were trying to do something else and got it wrong.
1phraseunintentionallyUnintentionally.
“I deleted the file by accident.”
2phraseby accidentBy chance rather than design.
“They found the passage entirely by accident.”
Also accepted in games: accidentally, by mistake
Practised in Everyday Adjectives, A Man Called Ove
First appears in chapter 18 of A Man Called Ove.
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