# Supremum and Infimum

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• September 10th 2008, 09:20 AM
hockey777
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.
• September 10th 2008, 09:27 AM
hockey777
Quick Thought, would I use density of rationals?
• September 10th 2008, 09:41 AM
Plato
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 $m = 1 \Rightarrow \quad \frac{1}{K} - \frac{1}{1} < - 1 + \varepsilon$.
• September 10th 2008, 09:49 AM
hockey777
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