ECE302S13Notes - Rhea

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}

1/9/13

S = {$ s_1,s_2,s_3 $}

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}