Erroneous means containing an error or mistake, or simply wrong. When you believe something erroneous, you believe something incorrect. If a newspaper prints an erroneous report that school is canceled when it actually isn't, students who read it might show up to empty classrooms or stay home when they should be in school.

The word comes from the same root as “error” but sounds more formal. You might say your friend made an error in their math homework, but a scientist would describe an erroneous conclusion in a research paper. An erroneous assumption is when you start with a wrong idea and build other thoughts on top of it, like assuming your friend is angry when they're actually just tired.

What makes something erroneous isn't that it sounds wrong or feels wrong, but that it simply doesn't match the facts. An erroneous belief might seem perfectly logical until you discover the truth. If you erroneously think the library closes at 6 PM when it actually closes at 5 PM, you might arrive to find locked doors, no matter how confident you felt about the closing time.