• 1. mistake and error: 声称由于出错
• 2. mathematical mistake and logic error: 数学与逻辑错误

• 1.The strict distinction of mistake and error results in the slower development of the research of mistake.
  失误与偏误两者的严格区分造成了对失误研究的相对滞后。
  dict.yoduao.com
• 2.Today, the IPCC said in a statement their error had been made "in good faith" and that after noticing the mistake, investigators issued a correction and "apologised directly to the family".
  今天，IPCC在一份声明中说，他们是因为“善意”才犯了错误，而且当注意到这个错误之后，调查员们发布了修正结果，并“直接对受害人家庭致以歉意”。
  dict.yoduao.com
• 3.Usually you can correct your error or just forget about it and move on. Making a mistake at work, however, can be more serious.
  通常情况下你可以改正你的错误或者乾脆忘掉它并继续前行。
  dict.yoduao.com

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