Partial ordering

**geezeela** · June 2nd 2011, 01:23 AM

Let X be the set of all real-valued functions x on the interval [0,1], and let $x\leqslant y mean x(t) \leqslant y(t) for all t\in [0,1]$ . show that this defines partial odering. Is it a total odering? does X have a maximal elements?

**girdav** · June 2nd 2011, 01:31 AM

What did you try? What do you have to show?

**geezeela** · June 5th 2011, 06:54 PM

yes i tried...but i could get started...please help me my friend

**girdav** · June 5th 2011, 10:39 PM

Let $x,y,z:\left[0,1\right]\rightarrow \mathbb R$ . You have to show that
a) $x\leqslant x$ ;
b) If $x\leqslant y$ and $y\leqslant x$ then $x(t)=y(t)\, \forall t\in:\left[0,1\right]$ ;
c) If $x\leqslant y$ and $y \leqslant z$ then $x\leqslant z$ .

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