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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?

  • Your example is ambiguous, but I think @ChuckLeviton has the idea. When you talk about correct instead of wrong formulas, a and the are more important to get right. If you were "using the correct formula" instead, using a means there is more than one way to solve the problem. Using the means there is only one way to solve the problem. When you speak in the negative (wrong formulas), saying the could be considered presumptuous. How could they know how many wrong ways there are to do something? I would consider this a forgivable error nonetheless. – MoondogsMaDawg Jul 6 '16 at 1:06
  • @ChristopherD. That was the logic I was lost in. You can say "the" to talk about that specific formula one is using, emphasizing THAT formula and singularity. However, I didn't know if using "a" is valid, but according to ChuckLeviton, it is not. If I am just referring to the formula and emphasizing the type of formula, which is the wrong type, I should be able to use "a", as there are an infinite number of wrong formulas you can possibly get. So why is using "a" invalid here? – guestIam Jul 6 '16 at 3:10
  • It depends on how specific the formula you are relating to is. If you are the speaker and are pointing out that "the" incorrect formula is used in step 3 out of 10, then that is the proper usage. But to say that out of 10 steps they used "the" incorrect formula is an error, because you did not specify which step was incorrect. It's in this instance that you use "a." "In step 3 you used the incorrect formula." (specific) "In your calculations you used an incorrect formula." (vague and ambiguous) (Both statements are proper usage) – MoondogsMaDawg Jul 6 '16 at 3:22
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    Related: 'A wrong answer' vs. 'the wrong answer' (on ELU SE) – CowperKettle Jul 6 '16 at 5:29
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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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In the example you cite, only the second usage is really valid. Even if there were multiple formulas that could be used to solve a problem and you used one that is none of these, you would still be "using the wrong formula".

If you say "using a wrong formula" it implies there are multiple wrong formulas and you are using one of those, not really what you want to say.

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    You said that if I use "'using a wrong formula' it implies there are multiple wrong formulas and you are using one of those" and it is not really what I want to say. Hm... I think it is still valid to use "a"... Is the reason that it is unlikely that I will say that because wrong formulas are indefinite? They are not a specific set of specific formulas; they can be anything, and there can be more than a million of those. It is not definite. Is it why that is? – guestIam Jul 6 '16 at 3:16
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If someone presents an algorithm which incorporates 27 different formulae, and one of those is incorrect, you could properly say "You're using a wrong formula."

However, if someone is presenting a scheme which involves only one formula, or if the questionable formula of a multiple-formula algorithm is currently under discussion, then you'd say "You're using the wrong formula."

You use "the" when the item of discussion has somehow been identified, "a" when it is anonymous.

(Similarly, if the entities are being discussed in plural, you use "the" if the entities are identified, and no article at all if anonymous: "You're using the wrong formulae" vs "You're using wrong formulae".)

(Pretty sure this has already been discussed several times, and this question is a dupe, but have not had much luck finding dupes of late.)

  • What if I say: "John, I have seen a lot of wrong formulas used by my students to calculate the Gibbs free energy of this reaction. You are using a wrong formula too, but a formula that I have never come across yet". – CowperKettle Jul 6 '16 at 4:48
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    @CowperKettle - That would be reasonable (I'd probably word it a bit differently). You are using "a wrong formula" since it's essentially a random selection from the set of wrong formulae, and this is the correct interpretation. – Hot Licks Jul 6 '16 at 11:50
  • Here's an example for you. A student is working on a big problem that involves your 27 different formulas. Somewhere in all of that is a mistake. A teacher who wants to give just a hint as to where the problem lies might say, "You're using a wrong formula." – fixer1234 Feb 27 '17 at 4:26

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