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Consider this statement.

A function F may have a derivative G which exists at every point, but is discontinuous at some point.

To which function does the phrase 'discontinuous at some point' refer to? F or G?

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    The English is ambiguous - it depends on whether the comma connects or disconnects. Maths-wise, though, I don’t think a function can have a derivative at a point of discontinuity, so the answer is G. – Lawrence Jun 21 at 10:21
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In the example "A function F may have a derivative G which exists at every point, but is discontinuous at some point,' the "which ..." is a relative clause modifying "derivative G", and so "which" must refer to that noun, "derivative G".

Since relative clauses can sometimes modify non-contiguous nouns, we should consider the possibility of an alternative interpretation with the relative clause actually modifying the noun of the subject "a function F", as in "A function F may exist which is discontinuous."

However, in such an example, "which" can refer only to the preceding non-contiguous "function F" because there is no intervening noun that the relative clause could modify. So far as I know, relative clauses always modify the first preceding noun which could be modified.

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Actually, in mathematics a fuction cannot have a derivative at a particular point without being continous at it. So technically, this phrase refers to the function G. But concerning the languange, I think that the comma plays a crutial role right here; and in order to fit the mathematical theory we should probably leave out it from the main sentence above. Because when we put it we make the emphasis on the fuction F and we consider talking about the function G as over.

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