This is an important question, Yun, and I'm glad you've brought it up.
When many people learn English, they get confused about when any
or a word containing any-
is negative or not negative. The simple truth is that any or a word containing any- is only negative when it comes after a negative verb
. Here are examples:I don't have any time to help you now.
She didn't know anybody at the party.
As you can see, because the two verbs in these sentences are negative, any
carry a negative meaning, too.
But when we use any
at the beginning of a sentence (without a negative verb before either of them) or when we use them in a yes/no question, they don't have a negative idea. They mean "this one, that one, or another one, etc." In other words, any
refer to somebody or something that's not specified. Here are some examples:Anybody who believes what he says is crazy!
Any time you need help, just call me, okay?
Do you have any questions?
Let's look at Swan's example again: Anyone can't do it.
The reason this is ungrammatical is that the sentence begins with anyone
, so it isn't negative in meaning; it means "this person or that person or another person, etc." But the verb is negative, so there's a conflict here. That's why Swan changed anyone
to no one
. And since the sentence now begins with a negative word, the verb can't be negative too since we don't use double negatives in English, so can't
has to be changed to can
I hope this explanation is clear enough for you, Yun.
As for your sentences, we need to make the same kinds of changes that Swan made in his example:
1) Any of them didn't come to the party. --> None
of them came
to the party.
2) Any other girls are not as pretty as Jane. --> None
of the girls is/are as pretty as Jane.
Now, let's go one step further. If we change the two statements above into yes/no questions, we can use any
1) Did any of them come to the party?
2) Are any other girls as pretty as Jane?