Error and Mistake
Error is a more formal word than mistake. But you can often use them interchangeably. For example, you can say:
Her homework is full of errors/mistakes.
But in certain fixed phrases, only one of these two nouns can be used.
Incorrect : It was a mistake of judgment.
Correct . It was an error of judgment.
Incorrect : I have done it by error.
Correct : I have done it by mistake. Or I have done it in error.
Besides, people often make mistakes accidentally or unwillingly but they have an error because of their ignorance.
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