# Partial ordering

• June 2nd 2011, 01:23 AM
geezeela
Partial ordering
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?
• June 2nd 2011, 01:31 AM
girdav
What did you try? What do you have to show?
• June 5th 2011, 06:54 PM
geezeela
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 $x\leqslant z$.