Can anyone offer advice on this problem below please - the text book I'm working with doesn't have any problems like this and I need a solution asap. Thanks in advance.
Construct a mapping B:N → N (natural numbers) such that the equation
B(n)=3nē has exactly three solutions.
For which elements n E N is the solution solved? (solutions must be in N)
Thanks again. Kinda makes sense now.
I'm stuck on one final question if anyone can help.
"A set P is said to be smaller than a set Q if there exists a mapping from P to Q, but there does not exist a mapping from Q to P. The notation P < Q is used to denote that P is smaller than Q according to this definition. Prove that, given sets P, Q, and R, if P<Q and Q<R, then P<R."
Any tips on how to solve this?
Muchos gracias amigos.
It should read: "A set P is said to be smaller than a set Q if there exists an injective mapping from P to Q, but there does not exist an injective mapping mapping from Q to P.
There is always a mapping from Q to P but cannot be injective if Q is more numerous than P.
The proof of the question just involves composition of mappings.