ECE302S13Notes - Rhea

1/9/13

If S is discrete and finite S = {s₁,s₂,s₃} S = {head,tail}, S = {win, lose}, S = {1,2,3,4,5,6}

If S is discrete but infinite,

S = {s₁,s₂,s₃,...} ex. S = {1,2,3,4,...}

    S = {sin(2π*440t),sin(2π*880t),sin(2π*1320t),...}
  Observe $ _{S = \mathbb{R}} $ is not routable; S = [0,1] is not routable
  S = {sin(2π*f*t)} f $ \in \mathbb{R} \geq $ 0 
    = {sin(2π*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} $= {0,3,e,π,-1,1.14,$ \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}

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