In English, when presented with a list (real or imagined) or answers that could be given to a question, and the correct one is not given, we will say that somebody has given "the wrong answer". However, doesn't "the" imply that there is only one wrong answer? Logically, it should be, "that's a wrong answer", not "that's the wrong answer"... right?
- Anybody can ask a question
- Anybody can answer
- The best answers are voted up and rise to the top
I know this is a language site, but seeing it from a mathematician's perspective you're totally right. You can expand any wrong answer by adding the statement "AND" plus another arbitrary wrong statement.
So technically there exists an unlimited number of wrong answers to the same question and technically you are right when saying that the reply should be "You have given a wrong answer".
The proper way to classify the wrong is even debated amongst linguists. Bernhard Schwarz of McGill University published a paper (pdf version) on this very subject as part of the 25th West Coast Conference on Formal Linguistics. The paper, Attributive Wrong, argued against the theory that the sentence "I opened the wrong bottle," is a syntactic reduction of the sentence "I opened the bottle that it was wrong for me to open." Schwarz's theory is that "non-local wrong is better analyzed as a separate lexical item, or possibly as part of complex determiner the wrong."
The current theories seem to be lacking if we consider the proposition offered in the original question: "In English, when presented with a list (real or imagined) or answers that could be given to a question, and the correct one is not given, we will say that somebody has given 'the wrong answer'."
It seems logical at first. What if the question were asked, "what is the capital city of Colombia?" A response of "London" might receive a reply of "that's the wrong answer." But what if the question were "what is one of the capital cities of South America?" It's unlikely that the reponse to a reply of "London" would be "that's the wrong answer." It would more probably be "that's a wrong answer" or "that's incorrect."
There is apparently some need for agreement between the article used for right answer and the article used for wrong answer. If there is only one correct answer, then "that's the right answer" or "that's the wrong answer" is used. When multiple answers are correct, it's either "that's a right answer" or "that's a wrong answer."