Learn English – “You’re using THE wrong formula” vs. “You’re using A wrong formula”: choosing between the definite and the indefinite article

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I'm trying to conceive the difference between the use of a definite article and an indefinite article here.

You are using a wrong formula (for the math problem).

You are using the wrong formula (for the math problem).

What's the difference if any?

Best Answer

The word "wrong" is an exception to the usual rules about "a" and "the". You almost always want to say "the wrong formula", not "a wrong formula", even if there are lots of possible formulas that are wrong.

Here's the best rule of thumb that I can think of. Imagine which of these questions a person would ask you: "Am I using the right formula?" or "Am I using a right formula?" If the question would use "the right", then the answer needs to use "the wrong"; if the question would use "a right", then the answer will use "a wrong".

Note that this rule only applies to the phrase "the wrong". Other ways of saying that something is wrong or incorrect use the usual rule, not the exceptional rule.

Examples:

Am I using the right formula?
No, you're using the wrong formula. (this is the only exceptional case)
No, you're using an incorrect formula.
No, you're using a completely wrong formula.
No, you're using a formula that's wrong.

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