mieux instead of meilleure

Question

Here's an example from your quiz: "Annette est meilleure en natation que Julie." Since we're referring to "swimming",  a verb...wouldn't we use "mieux" here instead of "meilleure?

Answer

Bonjour Helen,
In a word, no.  Mieux is an adverb that modifies: a  verb, an adjective or another adverb (if I recall correctly).  In the phrase: «Annette est meilleure en natation que Julie.», la natation is a noun which, in turn requires an adjective not an adverb, hence the use of meilleure.  Also the adjective is modifying Annette by describing her as better.  
«- Meilleur/meilleure is the comparative form of the adjective bon/bonne
- Mieux is the comparative form of the adverb bien.»
a simple phrase such as «Annette est bonne en natation» --> Annette is good in swimming.
Now let's take a look at this phrase.
Annette swims better than Julie -->  Annette nage mieux que Julie.  From this phrase we see that «mieux» is used in an adverbial sense.
Adverb use in French follows basically the same rules as it does in English grammar.
J'espère que ma réponse vous aiderait.
Bonne chance et bonne continuation dans vos études en français, la langue de Molière et qui a été utilisé par le monde français depuis l’époque d’Hugues Capet

Answer

OK. I thought "en natation" was a verb, meaning "swimming".     Since it's a noun meillure makes since.  Thanks.

Answer

Ron explained it quite well. Maybe juxtaposing two examples will help here:

Anne est meilleure en natation : Anne is "the better one" in swimming = Ann is the better swimmer. Clearly, meilleure modifies the person, Anne, and hence needs to be an adjective.

Anne nage mieux : Anne swims better. Here mieux modifies the verb (to swim) and therefore we need the adverb (mieux) and not the adjective (meilleure).

-- Chris (not a native speaker).

Answer

Darn, I just realized that Ron has pretty much given these two examples. Sorry for doubleposting.

-- Chris.