Cantor's Theorem (real analysis)

[KevinL]

Google has my particular homework online. I am doing 1.5.6, 1.5.7, 1.5.8

On 1.5.6 a), I created a function f(x) such that {a} if x = a, {b} if x = b, {c} if x=c. This is 1-1 since each element of A gets mapped to something different. Its obviously not onto.

Skipping down to 1.5.7, I need to create the set B for this function. For any a, it can't be an element of f(a). Does this mean B = the empty set?

If so, I think I can tackle the rest...

 

[hunt_mat]

If you want help, then I suggest you post your question here. We're not going to do an in depth google search to find your homework.

 

[KevinL]

Uhg, sorry. Thought I had google hyperlinked. http://books.google.com/books?id=7t...erent 1-1 mappings from A into P(A)"&f=false" is the link.

 

[Office_Shredder]

In this case B is going to be the empty set