- #1
playboy
The question is:
" Prove that if S is denumerable, then S is equinumerous with a proper subset of itself"
To begin, I am confused with the term denumerable because the textbook gives some diagram which is throwing me off. So can somebody clarify this for me:
A set S is denumerable if S and N (natural numbers) are equinumerous. That is, their is a BIJECTIVE function f: N---->S
The textbook says N is INFINITE. So if N is infite, that means that S HAS TO BE INFINTE if S is denumerable?
Now I'm reading the books diagram like this:
Countable sets are FINITE OR DENUMERABLE
Infinite sets are UNCOUNTABLE OR DENUMERABLE
So is this true: "if a set S is denumerable, then it HAS TO BE INFINITE?"
" Prove that if S is denumerable, then S is equinumerous with a proper subset of itself"
To begin, I am confused with the term denumerable because the textbook gives some diagram which is throwing me off. So can somebody clarify this for me:
A set S is denumerable if S and N (natural numbers) are equinumerous. That is, their is a BIJECTIVE function f: N---->S
The textbook says N is INFINITE. So if N is infite, that means that S HAS TO BE INFINTE if S is denumerable?
Now I'm reading the books diagram like this:
Countable sets are FINITE OR DENUMERABLE
Infinite sets are UNCOUNTABLE OR DENUMERABLE
So is this true: "if a set S is denumerable, then it HAS TO BE INFINITE?"