1) Prove that if the sets S-T and T-S are equivalent, then S and T are equivalent.
2) Prove that
$$ sup\{r \in Q : r

Question

1) Prove that if the sets S-T and T-S are equivalent, then S and T are equivalent.
2) Prove that 
$$ sup\{r \in Q : r< \sqrt{5} \}=\sqrt{5} $$

anonymous · Answer

i am not sure what the first one means, but the idea for the second one is this: 
suppose by way of contradiction that the supremum is less than $\sqrt{5}$ say it is $\sqrt{5}-\epsilon$
then since we know that between any two reals there is a rational, there exist some rational $r$ with  between $\sqrt{5}-\epsilon<r<\sqrt{5}$ contradicting the assumption that $\sqrt{5}-\epsilon$ is the supremum)

anonymous · Answer

thank you satellite, this helped me a lot..