# Math Help - Supremum and Infimum

1. ## Supremum and Infimum

I need to find the inf(S) and sup(S)

I know that they are -1 and 1. I know how to show that both of these are upper bounds. For example in the case of the Supremum, I don't know how to show that v<1 there exists a x>v for some x in S.

2. Quick Thought, would I use density of rationals?

3. It is true that $\left( {\varepsilon > 0} \right)\left[ {\exists K \mathrel\backepsilon \quad \frac{1}{K} < \varepsilon } \right]$

Now $n = 1 \Rightarrow \quad \frac{1}{1} - \frac{1}{K} > 1 - \varepsilon$ and $m = 1 \Rightarrow \quad \frac{1}{K} - \frac{1}{1} < - 1 + \varepsilon$.

4. ....