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I am writing my thesis and my advisor made a correction to the sentence below:

Transitional Rule commonly denoted by $\phi$ is defined by the map $\Sigma^n \rightarrow \Sigma$.

He has changed the sentence by changing the definite article the to the indefinite article a as below:

Transitional Rule commonly denoted by $\phi$ is defined by a map $\Sigma^n \rightarrow \Sigma$.

Which of the sentences above are correct providing that $\Sigma$ is a set that is defined previously and n is the length of a string?

I have already asked this question in English Stack Exchange and I could not get any answer. They have said this a technical question. Thanks in advance.

Yousof
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    If there is only one map, then say "the map". If there is more than one map, and your rule is defined by one of them, say "a map". – GEdgar Feb 05 '15 at 13:22
  • @GitGud, this is the first occurrence of the definition. – Yousof Feb 05 '15 at 13:23
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    @Yousof If there's nothing missing in the definition, then it should be 'a map', because there are many functions from $\Sigma ^n$ to $\Sigma$ (for $n>1$). – Git Gud Feb 05 '15 at 13:24
  • @GitGud, thanks for your response. The thing that I think the should be used is that, although there are different functions, but this map defines a specific way to define the rule $\phi$. – Yousof Feb 05 '15 at 13:36
  • @GEdgar may I also know your opinion about the comment above? – Yousof Feb 05 '15 at 13:39
  • @Yousof But you haven't described what that map is, just that it is a map from $\Sigma^n$ to $\Sigma$. – mrp Feb 05 '15 at 13:40
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    I agree with GitGud. – GEdgar Feb 05 '15 at 13:41
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    @Yousof "Binary relation on a given set $A$ commonly denoted by $\text{whatever}$ is the defined by the subset $R$ of $A^2$". Do you also think 'the' is appropriate here? If so, then I suggest you just change the wording completely to something like "A transitional rule, commonly denoted by $\phi$, is any map from $\Sigma ^n$ to $\Sigma$". – Git Gud Feb 05 '15 at 13:43
  • @GitGud Thanks you clarified it for me. – Yousof Feb 05 '15 at 13:46

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