## cinar 3 years ago 1) Prove that if the sets S-T and T-S are equivalent, then S and T are equivalent. 2) Prove that $sup\{r \in Q : r< \sqrt{5} \}=\sqrt{5}$

1. satellite73

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)

2. cinar

thank you satellite, this helped me a lot..