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     S = {sin(2<math>\pi</math>*440t),sin(2<math>\pi</math>*880t),sin(2<math>\pi</math>*1320t),...}
 
     S = {sin(2<math>\pi</math>*440t),sin(2<math>\pi</math>*880t),sin(2<math>\pi</math>*1320t),...}
 
     Observe <math>_{S = \mathbb{R}}</math> is not routable; S = [0,1] is not routable
 
     Observe <math>_{S = \mathbb{R}}</math> is not routable; S = [0,1] is not routable
            S = {sin(2<math>\pi</math>*f*t)} f <math>\in \mathbb{R} \geq</math> 0  
+
    S = {sin(2<math>\pi</math>*f*t)} f <math>\in \mathbb{R} \geq</math> 0  
              = {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>}
  
 
<math>\mathbb{Z}</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 <math>\mathbb{Z}</math>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 <math>\mathbb{R}</math>
  
= {0,3,e,,-1,1.14,, }
+
= {0,3,e,<math>\pi</math>,-1,1.14,<math>\sqrt{2}</math>}
  
 
Many different ways to write a set
 
Many different ways to write a set
[0,1] = {xsuch that(s. t.) 0x 1}
+
[0,1] = {x <math>\in \mathbb{R} </math>such that(s. t.) 0<math>\leq x \leq</math> 1}
 
={real positive numbers no greater than 1 as well as 0}
 
={real positive numbers no greater than 1 as well as 0}

Revision as of 18:04, 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 $ \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}

Alumni Liaison

Ph.D. on Applied Mathematics in Aug 2007. Involved on applications of image super-resolution to electron microscopy

Francisco Blanco-Silva