Use the Schröder-Bernstein theorem to show that there is a bijection between two intervals $[0,1]\subseteq \Bbb R$ and $[1,\infty)\subseteq \Bbb R$, thus they have the same cardinality.
What about the sets $(0,5)$ and $(10,20)$? Is there a bijection between them? (Don't need the Schröder-Bernstein theorem here). Similarly, consider $[0,\infty)$ and $[1,\infty)$.
Hello, this is a question from my practice final. Can anyone explain how to answer this question? As I understand, the theorem allows you to find a one-to-one function between two intervals to show that they have same cardinality, but I don't know how to apply this. For example, for the first question, is it simple as a function like $f(x) = 1/x$ or is there something more than that?
No comments:
Post a Comment