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Are both valid? I think the first is the only option, but I have been challenged on this and I can't explain exactly why the second is wrong. It does make sense, I suppose.

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possible duplicate of Is it: My apples and orange are/is wrong? – Andrew Leach Jan 25 '13 at 22:49
possible duplicate of Using "are/is" after a list with "and/or" – FumbleFingers Jan 26 '13 at 1:54

If you use is, then you are implicitly treating the compound noun changing and improving as a single, grouped set. Which makes the sentence have the form X is not the same thing, which naturally leads to the question "X is not the same thing as WHAT?"

Clearly the intention is for you to compare changing to improving, so they are really two separate items; and therefore you need to use the plural are to make it clear that you are comparing them, individually, to each other.

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Yes - contrast Tom and Jerry were always fighting with Tom and Jerry was my dad's favourite cartoon. – Edwin Ashworth Jan 26 '13 at 0:14
@EdwinAshworth Though that's more a matter of threating a plural as a singular because it's a title. Comparable: Cats are always fighting and Cats is my mum's favourite musical, respectively. – Jon Hanna Jan 26 '13 at 0:24
Thank you both for your answers – jonathan Jan 26 '13 at 18:10
@Jon Hanna - I'd say it's more fundamentally treating a singular concept, whether the corresponding noun appears in singular or plural form, as a construct requiring singular agreement. Plays, books, shows etc would be one subset of such concepts - but so would composites (fish and chips is my favourite meal) and collectives considered as wholes (the team was founded in 1896 - contrast the team were all tired after the match, with notional concord). – Edwin Ashworth Jan 27 '13 at 0:45

Mismatches in grammatical number are tricky, and have no perfect solution that will meet with total agreement.

This though is not an example of that. Your sentence is of the structure:

[noun phrase] [third person simple present tense of to be] not always the same thing [elided "as each other"].

The third person simple present tense of to be will be either singular or plural depending on the grammatical number of the noun phrase.

The noun phrase "Changing and improving" is a plural noun phrase formed from two singular nouns joined by and.

So the correct form of the sentence is:

Changing and improving are not always the same thing.

We don't match the verb to the word before it, we match it to the phrase before it. The phrase is plural, and so must the verb be.

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