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Revision as of 05:40, 15 April 2013
Note: this is the first of many pages to be uploaded.
1/9/13
If S is discrete and finite S = {$ s_1,s_2,s_3 $} S = {head,tail}, S = {win, lose}, S = {1,2,3,4,5,6}
If S is discrete but infinite,
S = {$ s_1,s_2,s_3 $,...} ex. S = {1,2,3,4,...}
S = {sin(2$ \pi $*440t),sin(2$ \pi $*880t),sin(2$ \pi $*1320t),...}
Observe $ _{S = \mathbb{R}} $ is not routable; S = [0,1] is not routable
S = {sin(2$ \pi $*f*t)} f $ \in \mathbb{R} \geq $ 0
= {sin(2$ \pi $*f*t)|0$ \leq f < \infty $}
$ \mathbb{Z} $ is all integers $ -\infty $ to $ \infty $ 
Is $ \mathbb{Z} $ routable? yes.
$ \mathbb{Z} $={0,1,-1,2,-2,3,-3, }as opposed to $ \mathbb{R} $
$ \mathbb{R} $= {0,3,e,$ \pi $,-1,1.14,$ \sqrt{2} $}
Many different ways to write a set [0,1] = {x $ \in \mathbb{R} $such that(s. t.) 0$ \leq x \leq $ 1} ={real positive numbers no greater than 1 as well as 0}
