About facebook mobile numbers?

[Virginia]

But what if i have not provided my number?

[blackgrumpycat]

I don't know. I haven't provided mine either and nothing has happened.

[pri✍]

Nothing will happen. FB ask your mobile number, just in case you're hacked, either your FB or your email you use for FB, or both, then FB can contact you through your mobile number.
But do remember, if for some reason you do not use that mobile number again, don't forget to update it with your new mobile number or delete it before then.