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               = {sin(2<math>\pi</math>*f*t)|0<math>\leq f < \infty</math>}
 
               = {sin(2<math>\pi</math>*f*t)|0<math>\leq f < \infty</math>}
  
is all integers <math>-\infty</math> to <math>\infty</math> 
+
<math>\mathbb{Z}</math> is all integers <math>-\infty</math> to <math>\infty</math> 
  
Is routable? yes.   
+
Is <math>\mathbb{Z}</math>routable? yes.   
 
={0,1,-1,2,-2,3,-3, }as opposed to 
 
={0,1,-1,2,-2,3,-3, }as opposed to 
  

Revision as of 17:35, 14 April 2013

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. ={0,1,-1,2,-2,3,-3, }as opposed to 

= {0,3,e,,-1,1.14,, }

Many different ways to write a set [0,1] = {xsuch that(s. t.) 0x 1} ={real positive numbers no greater than 1 as well as 0}

Alumni Liaison

Ph.D. 2007, working on developing cool imaging technologies for digital cameras, camera phones, and video surveillance cameras.

Buyue Zhang