Analysis Help - Could Anyone Please Assist with These Problems?

[buzzmath]

Could anyone please help with these problems?

1. show that the denumerable union of denumerable sets is denumerable.

2. show that for all finite d, N^d is denumerable.

3. Let k be a symmetric convex set in R^p. show that the functional below is a norm.
||x|| subscript k = inf t>= 0 {t: x an element of tk}

Thanks everyone

 

[Hurkyl]

Don't double post.

How far have you gotten on the problem?

 

[buzzmath]

I eventually figured them out. Thanks though.